Tarjan, Robert E. (Robert Endre) 1948
Overview
Works:  119 works in 369 publications in 4 languages and 2,316 library holdings 

Roles:  Author, Contributor, Opponent 
Classifications:  QA164, 511.6 
Publication Timeline
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Most widely held works about
Robert E Tarjan
 A generalization of Tarjan's depth first search algorithm for the biconnectivity problem by Yung Hyang Tsin( Book )
 Tarjan, Robert Endre : computer science( )
Most widely held works by
Robert E Tarjan
Notes on introductory combinatorics by
George Pólya(
Book
)
29 editions published between 1983 and 2010 in English and German and held by 684 WorldCat member libraries worldwide
Developed from the authors{u2019} introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya{u2019}s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths. This introduction will provide students with a solid foundation in the subject.  "This is a delightful little paperback which presents a daybyday transcription of a course taught jointly by Pólya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting minitextbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the Birkhäuser publishers produced a very pleasant text. One can count on [Pólya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory{u2026}[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading." {u2014}Mathematical Reviews (Review of the original hardcover edition) "The mathematical community welcomes this book as a final contribution to honour the teacher G. Pólya." {u2014}Zentralblatt MATH (Review of the original hardcover edition)
29 editions published between 1983 and 2010 in English and German and held by 684 WorldCat member libraries worldwide
Developed from the authors{u2019} introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya{u2019}s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths. This introduction will provide students with a solid foundation in the subject.  "This is a delightful little paperback which presents a daybyday transcription of a course taught jointly by Pólya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting minitextbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the Birkhäuser publishers produced a very pleasant text. One can count on [Pólya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory{u2026}[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading." {u2014}Mathematical Reviews (Review of the original hardcover edition) "The mathematical community welcomes this book as a final contribution to honour the teacher G. Pólya." {u2014}Zentralblatt MATH (Review of the original hardcover edition)
Data structures and network algorithms by
Robert E Tarjan(
Book
)
40 editions published between 1983 and 2014 in 4 languages and held by 627 WorldCat member libraries worldwide
Publisher description: "There has been an explosive growth in the field of combinatorial algorithms. These algorithms depend not only on results in combinatorics and especially in graph theory, but also on the development of new data structures and new techniques for analyzing algorithms. Four classical problems in network optimization are covered in detail, including a development of the data structures they use and an analysis of their running time. Data Structures and Network Algorithms attempts to provide the reader with both a practical understanding of the algorithms, described to facilitate their easy implementation, and an appreciation of the depth and beauty of the field of graph algorithms. "
40 editions published between 1983 and 2014 in 4 languages and held by 627 WorldCat member libraries worldwide
Publisher description: "There has been an explosive growth in the field of combinatorial algorithms. These algorithms depend not only on results in combinatorics and especially in graph theory, but also on the development of new data structures and new techniques for analyzing algorithms. Four classical problems in network optimization are covered in detail, including a development of the data structures they use and an analysis of their running time. Data Structures and Network Algorithms attempts to provide the reader with both a practical understanding of the algorithms, described to facilitate their easy implementation, and an appreciation of the depth and beauty of the field of graph algorithms. "
Efficiency of the network simplex algorithm for the maximum flow problem by
Andrew V Goldberg(
Book
)
8 editions published between 1988 and 1989 in English and held by 21 WorldCat member libraries worldwide
Goldfarb and Hao have proposed a network simplex algorithm that will solve a maximum flow problem on an nvertex, marc network in at most nm pivots and O(n squared m) time. In this paper we describe how to implement their algorithm to run in O(nmlog n) time by using an extension of the dynamic tree data structure of Sleator and Tarjan. This bound is less than a logarithmic factor larger than that of any other known algorithm for the problem. Keywords: Algorithms; Complexity; Data structures; Dynamic trees; Graphs; Linear programming; Maximum flow; Network flow; Network optimization
8 editions published between 1988 and 1989 in English and held by 21 WorldCat member libraries worldwide
Goldfarb and Hao have proposed a network simplex algorithm that will solve a maximum flow problem on an nvertex, marc network in at most nm pivots and O(n squared m) time. In this paper we describe how to implement their algorithm to run in O(nmlog n) time by using an extension of the dynamic tree data structure of Sleator and Tarjan. This bound is less than a logarithmic factor larger than that of any other known algorithm for the problem. Keywords: Algorithms; Complexity; Data structures; Dynamic trees; Graphs; Linear programming; Maximum flow; Network flow; Network optimization
Network flow algorithms by
Andrew V Goldberg(
Book
)
7 editions published in 1989 in English and German and held by 20 WorldCat member libraries worldwide
Network flow problems are central problems in operations research, computer science, and engineering and they arise in many real world applications. Starting with early work in linear programming and spurred by the classic book of Ford and Fulkerson, the study of such problems has led to continuing improvements in the efficiency of network flow algorithms. In spite of the long history of this study, many substantial results have been obtained within the last several years. In this survey we examine some of these recent developments and the ideas behind them. We discuss the classical network flow problems, the maximum flow problem and the minimumcost circulation problem, and a less standard problem, the generalized flow problem, sometimes called the problem of flows with losses and gains. The survey contains six chapters in addition to this introduction. Chapter 1 develops the terminology needed to discuss network flow problems. Chapter 2 discusses the maximum flow problem, and Chapters 3, 4, and 5 discuss different aspects of the minimumcost circulation problem, and Chapter 6 discusses the generalized flow problem. In the remainder of this introduction, we mention some of the history of network flow research, comment on some of the results to be presented in detail in later sections, and mention some results not covered in this survey. We are interested in algorithms whose running time is small as a function of the size of the network and the numbers involved (e.g. capacities, costs, or gains). (KR)
7 editions published in 1989 in English and German and held by 20 WorldCat member libraries worldwide
Network flow problems are central problems in operations research, computer science, and engineering and they arise in many real world applications. Starting with early work in linear programming and spurred by the classic book of Ford and Fulkerson, the study of such problems has led to continuing improvements in the efficiency of network flow algorithms. In spite of the long history of this study, many substantial results have been obtained within the last several years. In this survey we examine some of these recent developments and the ideas behind them. We discuss the classical network flow problems, the maximum flow problem and the minimumcost circulation problem, and a less standard problem, the generalized flow problem, sometimes called the problem of flows with losses and gains. The survey contains six chapters in addition to this introduction. Chapter 1 develops the terminology needed to discuss network flow problems. Chapter 2 discusses the maximum flow problem, and Chapters 3, 4, and 5 discuss different aspects of the minimumcost circulation problem, and Chapter 6 discusses the generalized flow problem. In the remainder of this introduction, we mention some of the history of network flow research, comment on some of the results to be presented in detail in later sections, and mention some results not covered in this survey. We are interested in algorithms whose running time is small as a function of the size of the network and the numbers involved (e.g. capacities, costs, or gains). (KR)
A parallel algorithm for finding a blocking flow in an acyclic network by
Andrew V Goldberg(
Book
)
8 editions published in 1988 in English and Undetermined and held by 16 WorldCat member libraries worldwide
We suppose a simple parallel algorithm for finding a blocking flow in an acyclic network. On an nvertex, marc network, our algorithm runs in O(n log n) time and O(nm) space using an mprocessor EREW PRAM. A consequence of our algorithm is an O(n2(log n)log(nC))time, O(nm)space, mprocessor algorithm for the minimumcost circulation problem, on a network with integer arc capacities of magnitude at most C. (KR)
8 editions published in 1988 in English and Undetermined and held by 16 WorldCat member libraries worldwide
We suppose a simple parallel algorithm for finding a blocking flow in an acyclic network. On an nvertex, marc network, our algorithm runs in O(n log n) time and O(nm) space using an mprocessor EREW PRAM. A consequence of our algorithm is an O(n2(log n)log(nC))time, O(nm)space, mprocessor algorithm for the minimumcost circulation problem, on a network with integer arc capacities of magnitude at most C. (KR)
An efficient planarity algorithm by
Robert E Tarjan(
Book
)
11 editions published between 1971 and 1979 in English and Undetermined and held by 12 WorldCat member libraries worldwide
An efficient algorithm is presented for determining whether a graph G can be embedded in the plane. Depthfirst search, or backtracking, is the most important of the techniques used by the algorithm. If G has V vertices, the algorithm requires O(V) space and O(V) time when implemented on a tandom access computer. An implementation on the Stanford IBM 360/67 successfully analyzed graphs with as many as 900 vertices in less than 12 seconds. (Author)
11 editions published between 1971 and 1979 in English and Undetermined and held by 12 WorldCat member libraries worldwide
An efficient algorithm is presented for determining whether a graph G can be embedded in the plane. Depthfirst search, or backtracking, is the most important of the techniques used by the algorithm. If G has V vertices, the algorithm requires O(V) space and O(V) time when implemented on a tandom access computer. An implementation on the Stanford IBM 360/67 successfully analyzed graphs with as many as 900 vertices in less than 12 seconds. (Author)
A unified approach to path problems by
Robert E Tarjan(
Book
)
7 editions published in 1979 in English and Undetermined and held by 10 WorldCat member libraries worldwide
We describe a general method for solving path problems on directed graphs. Such path problems include finding shortest paths, solving sparse systems of linear equations, and carrying out global flow analysis of computer programs. Our method consists of two steps. First, we construct a collection of regular expressions representing sets of paths in the graph. This can be done by using any standard algorithm, such as Gaussian or GaussJordon elimination. Next, we apply a natural mapping from regular expressions into the given problem domain. We exhibit the mappings required to find shortest paths, solve sparse systems of linear equations, and carry out global flow analysis. Our results provide a generalpurpose algorithm for solving any path problem, and show that the problem of constructing path expressions is in some sense the most general path problem. (Author)
7 editions published in 1979 in English and Undetermined and held by 10 WorldCat member libraries worldwide
We describe a general method for solving path problems on directed graphs. Such path problems include finding shortest paths, solving sparse systems of linear equations, and carrying out global flow analysis of computer programs. Our method consists of two steps. First, we construct a collection of regular expressions representing sets of paths in the graph. This can be done by using any standard algorithm, such as Gaussian or GaussJordon elimination. Next, we apply a natural mapping from regular expressions into the given problem domain. We exhibit the mappings required to find shortest paths, solve sparse systems of linear equations, and carry out global flow analysis. Our results provide a generalpurpose algorithm for solving any path problem, and show that the problem of constructing path expressions is in some sense the most general path problem. (Author)
Complexity of combinatorial algorithms by
Robert E Tarjan(
Book
)
9 editions published between 1976 and 1977 in English and Undetermined and held by 10 WorldCat member libraries worldwide
This paper examines recent work on the complexity of combinatorial algorithms, highlighting the aims of the work, the mathematical tools used, and the important results. Included are sections discussing ways to measure the complexity of an algorithm, methods for proving that certain problems are very hard to solve, tools useful in the design of good algorithms, and recent improvements in algorithms for solving ten representative problems. The final section suggests some directions for future research. (Author)
9 editions published between 1976 and 1977 in English and Undetermined and held by 10 WorldCat member libraries worldwide
This paper examines recent work on the complexity of combinatorial algorithms, highlighting the aims of the work, the mathematical tools used, and the important results. Included are sections discussing ways to measure the complexity of an algorithm, methods for proving that certain problems are very hard to solve, tools useful in the design of good algorithms, and recent improvements in algorithms for solving ten representative problems. The final section suggests some directions for future research. (Author)
Short encodings of evolving structures by
Daniel D Sleator(
Book
)
4 editions published between 1990 and 1991 in English and held by 10 WorldCat member libraries worldwide
We show for example that [omega](n log n) applications of the associative and commutative laws are required in the worst case to transform an nvariable expression over a binary associative, commutative operation into some other equivalent expression. Similarly, we show that [omega](n log n) 'diagonal flips' are required in the worst case to transform one nvertex numbered triangulated planar graph into some other one. Both of these lower bounds have matching upper bounds. An O(n log n) upper bound for associative, commutative operations was known previously, whereas we obtain here an O(n log n) upper bound for diagonal flips."
4 editions published between 1990 and 1991 in English and held by 10 WorldCat member libraries worldwide
We show for example that [omega](n log n) applications of the associative and commutative laws are required in the worst case to transform an nvariable expression over a binary associative, commutative operation into some other equivalent expression. Similarly, we show that [omega](n log n) 'diagonal flips' are required in the worst case to transform one nvertex numbered triangulated planar graph into some other one. Both of these lower bounds have matching upper bounds. An O(n log n) upper bound for associative, commutative operations was known previously, whereas we obtain here an O(n log n) upper bound for diagonal flips."
A Fast Algorithm for finding Dominators in a Flow Graph by
T Lengauer(
Book
)
7 editions published between 1978 and 1987 in English and held by 9 WorldCat member libraries worldwide
This paper presents a fast algorithm for finding dominators in a flow graph. The algorithm uses depthfirst search and an efficient method of computing functions defined on paths in trees. A simple implementation of the algorithm runs in O(m log n) time, where m is the number of edges and n is the number of vertices in the problem graph. A sophisticated implementation runs in O(M alpha (m, n)) time, where alpha(m, n) is a functional inverse of Ackermann's function. Both versions of the algorithm were implemented in Algol W, and tested on an IBM 370/168. The programs were compared with an implementation by Purdom and Moore of a straightforward O(mn)  time algorithm, and with a bit vector algorithm. The fast algorithm beat the straightforward algorithm and the bit vector algorithm on all but the smallest graphs tests
7 editions published between 1978 and 1987 in English and held by 9 WorldCat member libraries worldwide
This paper presents a fast algorithm for finding dominators in a flow graph. The algorithm uses depthfirst search and an efficient method of computing functions defined on paths in trees. A simple implementation of the algorithm runs in O(m log n) time, where m is the number of edges and n is the number of vertices in the problem graph. A sophisticated implementation runs in O(M alpha (m, n)) time, where alpha(m, n) is a functional inverse of Ackermann's function. Both versions of the algorithm were implemented in Algol W, and tested on an IBM 370/168. The programs were compared with an implementation by Purdom and Moore of a straightforward O(mn)  time algorithm, and with a bit vector algorithm. The fast algorithm beat the straightforward algorithm and the bit vector algorithm on all but the smallest graphs tests
Randomized parallel algorithms for trapezoidal diagrams by
Kenneth W Clarkson(
Book
)
3 editions published in 1991 in English and held by 8 WorldCat member libraries worldwide
For a set of segments forming K chains, we give an algorithm requiring O(A + n log* n + K log n) expected work and O(log n log log n log* n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps."
3 editions published in 1991 in English and held by 8 WorldCat member libraries worldwide
For a set of segments forming K chains, we give an algorithm requiring O(A + n log* n + K log n) expected work and O(log n log log n log* n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps."
Variations of a pebble game on graphs by
John R Gilbert(
Book
)
7 editions published in 1978 in English and Undetermined and held by 8 WorldCat member libraries worldwide
Two variations are examined of a oneperson pebble game played on directed graphs, which has been studied as a model of register allocation. The blackwhite pebble game of Cook and Sethi is shown to require as many pebbles in the worst case as the normal pebble game, to within a constant factor. For another version of the pebble game, the problem of deciding whether a given number of pebbles is sufficient for a given graph is shown to be complete in polynomial space
7 editions published in 1978 in English and Undetermined and held by 8 WorldCat member libraries worldwide
Two variations are examined of a oneperson pebble game played on directed graphs, which has been studied as a model of register allocation. The blackwhite pebble game of Cook and Sethi is shown to require as many pebbles in the worst case as the normal pebble game, to within a constant factor. For another version of the pebble game, the problem of deciding whether a given number of pebbles is sufficient for a given graph is shown to be complete in polynomial space
Finding minimumcost circulations by canceling negative cycles by
Andrew V Goldberg(
Book
)
4 editions published in 1987 in English and held by 8 WorldCat member libraries worldwide
A classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc. We show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm. This gives a very simple strongly polynomial algorithm that uses no scaling. A variant of the algorithm that uses dynamic trees runs in 0(nm(log n)min(log(nC), mlogn)) time on a network of n vertices, m arcs, and arc costs of maximum absolute value C. This bound is comparable to those of the fastest previously known algorithms. Keywords: Network flows, Minimum cost flow, Combinatorial optimization
4 editions published in 1987 in English and held by 8 WorldCat member libraries worldwide
A classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc. We show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm. This gives a very simple strongly polynomial algorithm that uses no scaling. A variant of the algorithm that uses dynamic trees runs in 0(nm(log n)min(log(nC), mlogn)) time on a network of n vertices, m arcs, and arc costs of maximum absolute value C. This bound is comparable to those of the fastest previously known algorithms. Keywords: Network flows, Minimum cost flow, Combinatorial optimization
Polygon triangulation in O (n log log n) time with simple data structures by D. G Kirkpatrick(
Book
)
4 editions published between 1990 and 1991 in English and held by 8 WorldCat member libraries worldwide
Abstract: "We give a new O (n log log n)time deterministic algorithm for triangulating simple nvertex polygons, which avoids the use of complicated data structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run in O (n log[superscript *] n) time. The major new techniques employed are the efficient location of horizontal visibility edges that partition the interior of the polygon into regions of approximately equal size, and a lineartime algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibilty partition of the entire chain
4 editions published between 1990 and 1991 in English and held by 8 WorldCat member libraries worldwide
Abstract: "We give a new O (n log log n)time deterministic algorithm for triangulating simple nvertex polygons, which avoids the use of complicated data structures. In addition, for polygons whose vertices have integer coordinates of polynomially bounded size, the algorithm can be modified to run in O (n log[superscript *] n) time. The major new techniques employed are the efficient location of horizontal visibility edges that partition the interior of the polygon into regions of approximately equal size, and a lineartime algorithm for obtaining the horizontal visibility partition of a subchain of a polygonal chain, from the horizontal visibilty partition of the entire chain
Finding minimumcost circulations by successive approximation by
Andrew V Goldberg(
Book
)
5 editions published in 1987 in English and held by 8 WorldCat member libraries worldwide
We develop a new approach to solving minimum cost circulation problems. Our approach combines methods for solving the maximum flow problems with successive approximation techniques based on cost scaling. We measure the accuracy of a solution by the amount that the complementary slackness conditions are violated. We propose a simple minimum cost circulation algorithm, one version of which runs in O(n3log(nC)) time on an nvertex network with integer arc costs of absolute value at most C. By incorporating sophisticated data structures into the algorithm, we obtain a time bound of O(nmlog(n2/m)log(nC)) on a network with m arcs. A slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of O(nlog(nC)) blocking flow problems. A corollary of this result is an O(n2(logn)log(nC)time, nprocessor parallel minimum cost circulation algorithm. Our approach also yields strongly polynomial minimum cost circulation algorithms. Our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem. We believe that a suitable implementation of our method will perform extremely well in practice. Keywords: Network flows, Minimum cost flow, Combinatorial optimization
5 editions published in 1987 in English and held by 8 WorldCat member libraries worldwide
We develop a new approach to solving minimum cost circulation problems. Our approach combines methods for solving the maximum flow problems with successive approximation techniques based on cost scaling. We measure the accuracy of a solution by the amount that the complementary slackness conditions are violated. We propose a simple minimum cost circulation algorithm, one version of which runs in O(n3log(nC)) time on an nvertex network with integer arc costs of absolute value at most C. By incorporating sophisticated data structures into the algorithm, we obtain a time bound of O(nmlog(n2/m)log(nC)) on a network with m arcs. A slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of O(nlog(nC)) blocking flow problems. A corollary of this result is an O(n2(logn)log(nC)time, nprocessor parallel minimum cost circulation algorithm. Our approach also yields strongly polynomial minimum cost circulation algorithms. Our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem. We believe that a suitable implementation of our method will perform extremely well in practice. Keywords: Network flows, Minimum cost flow, Combinatorial optimization
Fast algorithms for solving path problems by
Robert E Tarjan(
Book
)
5 editions published in 1979 in English and held by 8 WorldCat member libraries worldwide
Let G = (V, E) be a directed graph with a distinguished source vertex s. The singlesource path expression problem is to find, for each vertex v, a regular expression P(s, v) which represents the set of all paths in G from s to v. A solution to this problem can be used to solve shortest path problems, solve sparse systems of linear equations, and carry out global flow analysis. We describe a method to compute path expressions by dividing G into components, computing path expressions on the components by Gaussian elimination, and combining the solutions. This method requires 0 (m alpha o(m, n)) time on a reducible flow graph, where n is the vertices in G, m is the number of edges in G, and alpha is a functional inverse of Ackermann's function. The method makes use of an algorithm for evaluating functions defined on paths in trees. A simplified version of the algorithm, which runs in 0(m log n) time on reducible flow graphs, is quite easy to implement and efficient in practice. (Author)
5 editions published in 1979 in English and held by 8 WorldCat member libraries worldwide
Let G = (V, E) be a directed graph with a distinguished source vertex s. The singlesource path expression problem is to find, for each vertex v, a regular expression P(s, v) which represents the set of all paths in G from s to v. A solution to this problem can be used to solve shortest path problems, solve sparse systems of linear equations, and carry out global flow analysis. We describe a method to compute path expressions by dividing G into components, computing path expressions on the components by Gaussian elimination, and combining the solutions. This method requires 0 (m alpha o(m, n)) time on a reducible flow graph, where n is the vertices in G, m is the number of edges in G, and alpha is a functional inverse of Ackermann's function. The method makes use of an algorithm for evaluating functions defined on paths in trees. A simplified version of the algorithm, which runs in 0(m log n) time on reducible flow graphs, is quite easy to implement and efficient in practice. (Author)
A fast merging algorithm by
Mark Robbin Brown(
Book
)
5 editions published in 1977 in English and held by 7 WorldCat member libraries worldwide
An algorithm which merges sorted lists is represented as balanced binary tree. If the lists have lengths m and n (m <or = n) then the merging procedure runs in 0 (m log n/m) steps, which is the same order as the lower bound on all comparisonbased algorithms for this problem. (Author)
5 editions published in 1977 in English and held by 7 WorldCat member libraries worldwide
An algorithm which merges sorted lists is represented as balanced binary tree. If the lists have lengths m and n (m <or = n) then the merging procedure runs in 0 (m log n/m) steps, which is the same order as the lower bound on all comparisonbased algorithms for this problem. (Author)
Recent developments in the complexity of combinatorial algorithms by
Robert E Tarjan(
Book
)
6 editions published in 1980 in English and Undetermined and held by 7 WorldCat member libraries worldwide
Several major advances in the area of combinatorial algorithms include improved algorithms for matrix multiplication and maximum network flow, a polynomialtime algorithm for linear programming, and steps toward a polynomialtime algorithm for graph isomorphism. This paper surveys these results and suggests directions for future research. Included is a discussion of recent work by the author and his students on dynamic dictionaries, network flow problems, and related questions
6 editions published in 1980 in English and Undetermined and held by 7 WorldCat member libraries worldwide
Several major advances in the area of combinatorial algorithms include improved algorithms for matrix multiplication and maximum network flow, a polynomialtime algorithm for linear programming, and steps toward a polynomialtime algorithm for graph isomorphism. This paper surveys these results and suggests directions for future research. Included is a discussion of recent work by the author and his students on dynamic dictionaries, network flow problems, and related questions
Improved time bounds for the maximum flow problem by
Ravindra K Ahuja(
Book
)
5 editions published between 1987 and 1988 in English and held by 7 WorldCat member libraries worldwide
A new approach is proposed to the maximum network flow problem. The approach yields a very simple algorithm running O(ncubed) time on nvertex networks. Incorporation of the dynamic tree data structure of Sleator and Tarjan yields a more complicated algorithm with a running time of O(nm log (nsquared/m)) on medge networks. A variant of the algorithm is developed that uses scaling and runs in O(nm + (nsq) log U) time on networks with integer edge capacities bounded by U. This paper obtains a modification of the AhujaOrlin algorithm with a running time of O(nm + (nsq) (log U)/(log log u). The use of dynamic trees in this algorithm further reduces the time bound on O(nm log (n log U/mlog log U + 2)). This result demonstrates that the combined use of scaling and dynamic trees results in speed not obtained by using either technique alone
5 editions published between 1987 and 1988 in English and held by 7 WorldCat member libraries worldwide
A new approach is proposed to the maximum network flow problem. The approach yields a very simple algorithm running O(ncubed) time on nvertex networks. Incorporation of the dynamic tree data structure of Sleator and Tarjan yields a more complicated algorithm with a running time of O(nm log (nsquared/m)) on medge networks. A variant of the algorithm is developed that uses scaling and runs in O(nm + (nsq) log U) time on networks with integer edge capacities bounded by U. This paper obtains a modification of the AhujaOrlin algorithm with a running time of O(nm + (nsq) (log U)/(log log u). The use of dynamic trees in this algorithm further reduces the time bound on O(nm log (n log U/mlog log U + 2)). This result demonstrates that the combined use of scaling and dynamic trees results in speed not obtained by using either technique alone
Proceedings of the tenth annual ACMSIAM symposium on Discrete algorithms by
Robert E Tarjan(
)
2 editions published in 1999 in English and held by 0 WorldCat member libraries worldwide
2 editions published in 1999 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Woods, Donald R. 1954
 Pólya, George 18871985 Author
 Society for Industrial and Applied Mathematics
 Goldberg, Andrew V. Author
 Stanford University Computer Science Department
 Sleator, Daniel D. (Daniel Dominic) 1953 Author
 Grigoriadis, Michael D.
 STANFORD UNIV CALIF Dept. of COMPUTER SCIENCE
 Tardos Éva
 PRINCETON UNIV NJ Dept. of COMPUTER SCIENCE
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Associated Subjects
Algebras, Linear Algorithms Approximation theory Binary system (Mathematics) Branch and bound algorithms Canada Coding theory Combinations Combinatorial analysis Combinatorial analysisData processing Compiling (Electronic computers) Computational complexity Computer algorithms Computer networks Computer science Computer scienceMathematics Computer software Data structures (Computer science) Electronic data processing Flowgraphs Fluid dynamics Games of strategy (Mathematics) Game theory Gauss maps Geometry, PlaneData processing Global analysis (Mathematics) Graph grammars Graph theory Graph theoryData processing Linear programming Machine theory Mappings (Mathematics) Mathematical optimization Mathematics Operations research Parallel algorithms Parallel processing (Electronic computers) Path analysis (Statistics) Polynomials Problem solving Program transformation (Computer programming) Scientists Sparse matrices Topology Trees (Graph theory) Triangulation United States
Alternative Names
Endre Tarjan Robert
Robert Tardžan
Robert Tarjan American computer scientist
Robert Tarjan Amerikaans wiskundige
Robert Tarjan amerikanischer Informatiker
Robert Tarjan amerikansk datavetare och matematiker
Robert Tarjan amerikansk informatikar og matematikar
Robert Tarjan amerikansk informatiker og matematiker
Robert Tarjan científico de la computación estadaounidense
Robert Tarjan informaticien américain
Robert Tarjan informatico statunitense
Robert Tarjan nhà nghiên cứu khoa học máy tính
Tarjan, R. E
Tarjan, Robert E.
Tarjan, Robert E. 1948
Tarjan, Robert E. (Robert Endre)
Tarjan, Robert E. (Robert Endre), 1948
Tarjan, Robert Endre
Tarjan, Robert Endre 1948
Роберт Андре Тар'ян
Роберт Тарџан
Тарьян, Роберт
רוברט טרג'אן
رابرت تارجان ریاضیدان و دانشمند علوم کامپیوتر آمریکایی
روبرت تارجان
রবার্ট টারজান
タージャン, R. E.
タージャン, ロバート E.
タルジャン, R. E.
ロバート・タージャン
羅伯特·塔揚
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