Tarjan, Robert E. (Robert Endre) 1948
Overview
Works:  120 works in 282 publications in 3 languages and 2,142 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Contributor 
Classifications:  QA164, 511.6 
Publication Timeline
.
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
)
25 editions published between 1983 and 2010 in 3 languages and held by 663 WorldCat member libraries worldwide
25 editions published between 1983 and 2010 in 3 languages and held by 663 WorldCat member libraries worldwide
Data structures and network algorithms by
Robert E Tarjan(
Book
)
29 editions published between 1983 and 1991 in 3 languages and held by 621 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. "
29 editions published between 1983 and 1991 in 3 languages and held by 621 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
)
7 editions published between 1988 and 1989 in English and held by 20 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(n2m) time. In this paper we describe how to implement their algorithm to run in O(nm log 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
7 editions published between 1988 and 1989 in English and held by 20 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(n2m) time. In this paper we describe how to implement their algorithm to run in O(nm log 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
Network flow algorithms by
Andrew V Goldberg(
Book
)
6 editions published in 1989 in English and German and held by 19 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)
6 editions published in 1989 in English and German and held by 19 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
)
5 editions published in 1988 in English and Undetermined and held by 12 WorldCat member libraries worldwide
We propose a simple parallel algorithm for finding a blocking flow in an acyclic network. On an nvertex, marc network, our algorithm runs in 0(n log n) time and 0(nm) space using an mprocessor EREW PRAM. A consequence of our algorithm is an 0(n²(log n)log(n(ʹ))time, 0(nm)space, mprocessor algorithm for the minimumcost circulation problem, on a network with integer arc capacities of magnitude at most C
5 editions published in 1988 in English and Undetermined and held by 12 WorldCat member libraries worldwide
We propose a simple parallel algorithm for finding a blocking flow in an acyclic network. On an nvertex, marc network, our algorithm runs in 0(n log n) time and 0(nm) space using an mprocessor EREW PRAM. A consequence of our algorithm is an 0(n²(log n)log(n(ʹ))time, 0(nm)space, mprocessor algorithm for the minimumcost circulation problem, on a network with integer arc capacities of magnitude at most C
Complexity of combinatorial algorithms by
Robert E Tarjan(
Book
)
8 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)
8 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)
A unified approach to path problems by
Robert E Tarjan(
Book
)
6 editions published in 1979 in English and Undetermined and held by 9 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)
6 editions published in 1979 in English and Undetermined and held by 9 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)
An efficient planarity algorithm by
Robert E Tarjan(
Book
)
8 editions published between 1971 and 1979 in English and Undetermined and held by 9 WorldCat member libraries worldwide
8 editions published between 1971 and 1979 in English and Undetermined and held by 9 WorldCat member libraries worldwide
Short encodings of evolving structures by
Daniel D Sleator(
Book
)
3 editions published between 1990 and 1991 in English and held by 9 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."
3 editions published between 1990 and 1991 in English and held by 9 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
)
6 editions published between 1978 and 1987 in English and Undetermined and held by 8 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
6 editions published between 1978 and 1987 in English and Undetermined and held by 8 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
)
2 editions published in 1991 in English and held by 7 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."
2 editions published in 1991 in English and held by 7 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
Stanford University(
Book
)
6 editions published in 1978 in English and Undetermined and held by 7 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
6 editions published in 1978 in English and Undetermined and held by 7 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
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
Recent developments in the complexity of combinatorial algorithms by
Robert E Tarjan(
Book
)
5 editions published in 1980 in English and Undetermined and held by 6 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
5 editions published in 1980 in English and Undetermined and held by 6 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
Polygon triangulation in O(n log log n) time with simple data structures by D. G Kirkpatrick(
Book
)
2 editions published between 1990 and 1991 in English and held by 6 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* 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 visibility partition of the entire chain
2 editions published between 1990 and 1991 in English and held by 6 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* 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 visibility partition of the entire chain
A fast merging algorithm by
M. R Brown(
Book
)
4 editions published in 1977 in English and held by 6 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)
4 editions published in 1977 in English and held by 6 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)
A linear time algorithm for finding an ambitus by
Bhubaneswar Mishra(
Book
)
2 editions published between 1989 and 1991 in English and held by 6 WorldCat member libraries worldwide
In order to achieve a good timecomplexity for such an algorithm employing the divideandconquer paradigm, it is necessary to find an ambitus quickly. We also show that, using ambitus, lineartime algorithms can be devised for abidingpathfinding and nonseparatinginducedcycle finding problems."
2 editions published between 1989 and 1991 in English and held by 6 WorldCat member libraries worldwide
In order to achieve a good timecomplexity for such an algorithm employing the divideandconquer paradigm, it is necessary to find an ambitus quickly. We also show that, using ambitus, lineartime algorithms can be devised for abidingpathfinding and nonseparatinginducedcycle finding problems."
Edgedisjoint spanning trees, dominators, and depthfirst search by
Robert E Tarjan(
Book
)
4 editions published in 1974 in English and Undetermined and held by 5 WorldCat member libraries worldwide
This paper presents an algorithm for finding two edgedisjoint spanning trees rooted at a fixed vertex of a directed graph. The algorithm uses depthfirst search, an efficient method for computing disjoint set unions, and an efficient method for computing dominators. It requires O(V log V+E) time and O(V+E) space to analyze a graph with V vertices and E edges. (Author)
4 editions published in 1974 in English and Undetermined and held by 5 WorldCat member libraries worldwide
This paper presents an algorithm for finding two edgedisjoint spanning trees rooted at a fixed vertex of a directed graph. The algorithm uses depthfirst search, an efficient method for computing disjoint set unions, and an efficient method for computing dominators. It requires O(V log V+E) time and O(V+E) space to analyze a graph with V vertices and E edges. (Author)
Almostoptimum parallel speedups of algorithms for bipartite matching and related problems by
Harold N Gabow(
Book
)
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Abstract: "This paper focuses on algorithms for matching problems that run on an EREW PRAM with p processors. Given is a bipartite graph with n verticies, m edges, and integral edge costs at most N in magnitude. An algorithm is presented for the assignment problem (minimum cost perfect bipartite matching) that runs in [formula] time and O(m) space, for [formula]. This bound is within a factor of log p of optimum speedup of the best known sequential algorithm, which in turn is within a factor of log(nN) of the best known bound for the problem without costs (maximum cardinality matching.) Extensions of the algorithms are given, including an algorithm for maximum cardinality bipartite matching with slightly better processor bounds, and similar results for bipartite degreeconstrained subgraph problems (with and without costs.)."
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Abstract: "This paper focuses on algorithms for matching problems that run on an EREW PRAM with p processors. Given is a bipartite graph with n verticies, m edges, and integral edge costs at most N in magnitude. An algorithm is presented for the assignment problem (minimum cost perfect bipartite matching) that runs in [formula] time and O(m) space, for [formula]. This bound is within a factor of log p of optimum speedup of the best known sequential algorithm, which in turn is within a factor of log(nN) of the best known bound for the problem without costs (maximum cardinality matching.) Extensions of the algorithms are given, including an algorithm for maximum cardinality bipartite matching with slightly better processor bounds, and similar results for bipartite degreeconstrained subgraph problems (with and without costs.)."
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
Annotation
2 editions published in 1999 in English and held by 0 WorldCat member libraries worldwide
Annotation
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Pólya, George 18871985 Author
 Woods, Donald R. 1954
 Society for Industrial and Applied Mathematics
 Goldberg, Andrew V. Author
 Stanford University Computer Science Department
 Grigoriadis, Michael D.
 Sleator, Daniel D. (Daniel Dominic) 1953 Author
 PRINCETON UNIV NJ DEPT OF COMPUTER SCIENCE
 STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
 Gabow, Harold N. Author
Useful Links
Associated Subjects
Algorithms 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 programming Computer science Computer scienceMathematics Computer software Data structures (Computer science) Electronic data processing Flowgraphs Games of strategy (Mathematics) Game theory Gauss maps Geometry, PlaneData processing Global analysis (Mathematics) Graph grammars Graphic methods Graph theory Graph theoryData processing Linear programming Machine theory Mappings (Mathematics) Matching theory Mathematical optimization Mathematics Multiprocessors 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 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 cientfico de la computacin estadaounidense
Robert Tarjan informaticien amricain
Robert Tarjan informatico statunitense
Robert Tarjan nh nghin cứu khoa học my tnh
Tarjan, Robert E.
Tarjan, Robert E. 1948
Tarjan, Robert E. (Robert Endre), 1948
Tarjan, Robert Endre.
Tarjan, Robert Endre 1948
Роберт Тарџан
Тарьян, Роберт
רוברט טרג'אן
رابرت تارجان ریاضیدان و دانشمند علوم کامپیوتر آمریکایی
روبرت تارجان
রবার্ট টারজান
タルジャン, R. E
ロバート・タージャン
羅伯特塔揚
Languages
Covers