Theory of 2-structures. Part II: representation through labeled tree families
Theoretical Computer Science
Text algorithms
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Construction of probe interval models
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Finding All Common Intervals of k Permutations
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
PC trees and circular-ones arrangements
Theoretical Computer Science - Computing and combinatorics
Linear-Time Recognition of Circular-Arc Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A certifying algorithm for the consecutive-ones property
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Linear-time modular decomposition of directed graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Journal of Computer and System Sciences
Using PQ trees for comparative genomics
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Computing common intervals of K permutations, with applications to modular decomposition of graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Revisiting t. uno and m. yagiura's algorithm
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Tree-representation of set families and applications to combinatorial decompositions
European Journal of Combinatorics
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Partitive set families are families of sets that can be quite large, but have a compact, recursive representation in the form of a tree. This tree is a common generalization of PQ trees, the modular decomposition of graphs, certain decompositions of boolean functions, and decompositions that arise on a variety of other combinatorial structures. We describe natural operators on partitive set families, give algebraic identities for manipulating them, and describe efficient algorithms for evaluating them. We use these results to obtain new time bounds for finding the common intervals of a set of permutations, finding the modular decomposition of an edge-colored graph (also known as a two-structure), finding the PQ tree of a matrix when a consecutive-ones arrangement is given, and finding the modular decomposition of a permutation graph when its permutation realizer is given.