45 research outputs found
Compressed Representations of Permutations, and Applications
We explore various techniques to compress a permutation over n
integers, taking advantage of ordered subsequences in , while supporting
its application (i) and the application of its inverse in
small time. Our compression schemes yield several interesting byproducts, in
many cases matching, improving or extending the best existing results on
applications such as the encoding of a permutation in order to support iterated
applications of it, of integer functions, and of inverted lists and
suffix arrays
Some results on triangle partitions
We show that there exist efficient algorithms for the triangle packing
problem in colored permutation graphs, complete multipartite graphs,
distance-hereditary graphs, k-modular permutation graphs and complements of
k-partite graphs (when k is fixed). We show that there is an efficient
algorithm for C_4-packing on bipartite permutation graphs and we show that
C_4-packing on bipartite graphs is NP-complete. We characterize the cobipartite
graphs that have a triangle partition
Fast RSK Correspondence by Doubling Search
The Robinson-Schensted-Knuth (RSK) correspondence is a fundamental concept in combinatorics and representation theory. It is defined as a certain bijection between permutations and pairs of Young tableaux of a given order. We consider the RSK correspondence as an algorithmic problem, along with the closely related k-chain problem. We give a simple, direct description of the symmetric RSK algorithm, which is implied by the k-chain algorithms of Viennot and of Felsner and Wernisch. We also show how the doubling search of Bentley and Yao can be used as a subroutine by the symmetric RSK algorithm, replacing the default binary search. Surprisingly, such a straightforward replacement improves the asymptotic worst-case running time for the RSK correspondence that has been best known since 1998. A similar improvement also holds for the average running time of RSK on uniformly random permutations
Stable Noncrossing Matchings
Given a set of men represented by points lying on a line, and
women represented by points lying on another parallel line, with each
person having a list that ranks some people of opposite gender as his/her
acceptable partners in strict order of preference. In this problem, we want to
match people of opposite genders to satisfy people's preferences as well as
making the edges not crossing one another geometrically. A noncrossing blocking
pair w.r.t. a matching is a pair of a man and a woman such that
they are not matched with each other but prefer each other to their own
partners in , and the segment does not cross any edge in . A
weakly stable noncrossing matching (WSNM) is a noncrossing matching that does
not admit any noncrossing blocking pair. In this paper, we prove the existence
of a WSNM in any instance by developing an algorithm to find one in a
given instance.Comment: This paper has appeared at IWOCA 201