Simple linear time recognition of unit interval graphs
Information Processing Letters
Randomized dynamic graph algorithms with polylogarithmic time per operation
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fully dynamic algorithms for chordal graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs
SIAM Journal on Computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
A fully dynamic algorithm for recognizing and representing chordal graphs
PSI'06 Proceedings of the 6th international Andrei Ershov memorial conference on Perspectives of systems informatics
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In this paper we study the problem of recognizing and representing dynamically changing proper interval graphs. The input to the problem consists of a series of modifications to be performed on a graph, where a modification can be a deletion or an addition of a vertex or an edge. The objective is to maintain a representation of the graph as long as it remains a proper interval graph, and to detect when it ceases to be so. The representation should enable one to efficiently construct a realization of the graph by an inclusion-free family of intervals. This problem has important applications in physical mapping of DNA.We give a near-optimal fully dynamic algorithm for this problem. It operates in time O(log n) per edge insertion or deletion. We prove a close lower bound of 驴(log n/(log log n + log b)) amortized time per operation in the cell probe model with word-size b. We also construct optimal incremental and decremental algorithms for the problem, which handle each edge operation in O(1) time.