Pittel, Boris
Overview
Works:  9 works in 16 publications in 1 language and 44 library holdings 

Roles:  Author, Thesis advisor 
Classifications:  QA76, 511.5 
Publication Timeline
.
Most widely held works by
Boris Pittel
Stable husbands
by
Donald Ervin Knuth(
Book
)
3 editions published in 1988 in English and held by 13 WorldCat member libraries worldwide
Suppose n boys and n girls rank each other at random. We show that any particular girl has at least (1/2[Eta])ln n and at least (1 + [Eta])ln n different husbands in the set of all Gale/Shapley stable matchings defined by these rankings, with probability approaching 1 as n [approaches] [infinity], if [Eta] is any positive constant. The proof emphasizes general methods that appear to be useful for the analysis of many other combinatorial algorithms
3 editions published in 1988 in English and held by 13 WorldCat member libraries worldwide
Suppose n boys and n girls rank each other at random. We show that any particular girl has at least (1/2[Eta])ln n and at least (1 + [Eta])ln n different husbands in the set of all Gale/Shapley stable matchings defined by these rankings, with probability approaching 1 as n [approaches] [infinity], if [Eta] is any positive constant. The proof emphasizes general methods that appear to be useful for the analysis of many other combinatorial algorithms
The average number of stable matchings
by
Boris Pittel(
Book
)
3 editions published in 1988 in English and held by 12 WorldCat member libraries worldwide
The probable behavior of an instance of size n of the stable marriage problem, chosen informaly at random, is studied. The expected number of stable matchings is shown to be asymptotic to e⁻¹n ln n for n [approaches] [infinity]. The total rank of women by men in the male optimal (pessimal) matching is proven to be close to n ln n (resp. n²/ln n), with high probability
3 editions published in 1988 in English and held by 12 WorldCat member libraries worldwide
The probable behavior of an instance of size n of the stable marriage problem, chosen informaly at random, is studied. The expected number of stable matchings is shown to be asymptotic to e⁻¹n ln n for n [approaches] [infinity]. The total rank of women by men in the male optimal (pessimal) matching is proven to be close to n ln n (resp. n²/ln n), with high probability
The first cycles in an evolving graph
by
P Flajolet(
Book
)
4 editions published in 1988 in English and held by 12 WorldCat member libraries worldwide
If successive connections are added at random to an initially disconnected set of n points, the expected length of the first cycle that appears will be proportional to n 1/6, with a standard deviation proportional to n 1/4. The size of the component containing this cycle will be of order n 1/2, on the average, with standard deviation of order n 7/12. The average length of the kth cycle is proportional to n 1/6(log n)k1. Furthermore, the probability is [square root of] 2/3 + 0(n 1/3) that the graph has no components with more than one cycle at the moment when the number of edges passes 1/2 n. These results can be proved with analytical methods based on combinatorial enumeration with multivariate generating functions, followed by contour integration to derive assymptotic functions for the quantities of interest
4 editions published in 1988 in English and held by 12 WorldCat member libraries worldwide
If successive connections are added at random to an initially disconnected set of n points, the expected length of the first cycle that appears will be proportional to n 1/6, with a standard deviation proportional to n 1/4. The size of the component containing this cycle will be of order n 1/2, on the average, with standard deviation of order n 7/12. The average length of the kth cycle is proportional to n 1/6(log n)k1. Furthermore, the probability is [square root of] 2/3 + 0(n 1/3) that the graph has no components with more than one cycle at the moment when the number of edges passes 1/2 n. These results can be proved with analytical methods based on combinatorial enumeration with multivariate generating functions, followed by contour integration to derive assymptotic functions for the quantities of interest
Sudden emergence of a giant kcore in a random graph
by
Boris Pittel(
Book
)
1 edition published in 1995 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 2 WorldCat member libraries worldwide
On likely solutions of a stable matching problem
by
Boris Pittel(
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Fast probabilistic algorithms for Hamilton circuits and matchings revisited
by
Boris Pittel(
Book
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
The average performance of the greedy matching algorithm
by
Martin Dyer(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
A study of random hypergraphs and directed graphs
by Daniel J Poole(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We establish and describe the likely structure of random hypergraph and directed graph models, expanding upon classical results that pertain to the likely structure of the random undirected graph models
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
We establish and describe the likely structure of random hypergraph and directed graph models, expanding upon classical results that pertain to the likely structure of the random undirected graph models
Stable husbands
by
Donald Ervin Knuth(
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
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