Counting the number of vertex covers in a trapezoid graph

Lin, Min-Sheng; Chen, Yung-Jui

doi:10.1016/j.ipl.2009.08.003

Cited by 10 publications

(11 citation statements)

References 18 publications

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“…Let N G [v] denote the closed neighborhood of vertex v in G. The following lemma [4] is required for the proof in Theorem 1.…”

Section: O(n 2 )-Time Algorithm For Counting Issmentioning

confidence: 99%

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Counting independent sets and its variation in cocomparability graphs

Su¹,

Lin²

2014

ams

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“…Let N G [v] denote the closed neighborhood of vertex v in G. The following lemma [4] is required for the proof in Theorem 1.…”

Section: O(n 2 )-Time Algorithm For Counting Issmentioning

confidence: 99%

“…Lin and Chen [4] presented O(n 2 ) time algorithms for counting VCs (or ISs), minimal VCs (or MISs) in a trapezoid graph with n vertices. This paper extends these results to cocomparability graphs, which is a superclass of trapezoid graphs.…”

Section: Introductionmentioning

confidence: 99%

Counting independent sets and its variation in cocomparability graphs

Su¹,

Lin²

2014

ams

Self Cite

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“…The problem of counting the vertex covers in a graph [13,16,18] is the following. Given a graph G = (V, E), how many subsets S ⊆ V constitute a vertex cover, where S is a vertex cover of G if for each uv ∈ E, either u ∈ S or v ∈ S. (We note that we are counting vertex covers and not minimum vertex covers.)…”

Section: Counting Vertex Covers In Unit Disk Graphsmentioning

confidence: 99%

Closest Pair and the Post Office Problem for Stochastic Points

Kamousi

Chan

Suri

2011

Lecture Notes in Computer Science

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Abstract. Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point mi ∈ M with an independent probability pi. How difficult is it to compute elementary statistics about the closest pair of points in such a subset? For instance, what is the probability that the distance between the closest pair of points in the random subset is no more than , for a given value ? Or, can we preprocess the master set M such that given a query point q, we can efficiently estimate the expected distance from q to its nearest neighbor in the random subset? We obtain hardness results and approximation algorithms for stochastic problems of this kind.

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“…For instance, in [9], some of the most classical problems in graph theory such as finding chromatic number, maximum weighted independent set, minimum clique cover and maximum weighted clique are solved in O(n log n) time by using their box representation and sweeping line techniques. Recently, by exploring the simplicity of this graph class, many well-known problems have a more efficient solution on trapezoid models, such as some O(n 2 ) algorithms for several counting problems on vertex covers [20], efficient algorithms on K-terminal residual reliability of d-trapezoid graphs [21,26], an O(n log n) algorithm for calculating the vertex connectivity [16].…”

Section: Introductionmentioning

confidence: 99%

Efficient maximum matching algorithms for trapezoid graphs

Le²,

2017

ejgta

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Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. Many NPhard problems can be solved in polynomial time if they are restricted on trapezoid graphs. A matching in a graph is a set of pairwise disjoint edges, and a maximum matching is a matching of maximum size. In this paper, we first propose an O(n(log n)3 ) algorithm for finding a maximum matching in trapezoid graphs, then improve the complexity to O(n(log n)2 ). Finally, we generalize this algorithm to a larger graph class, namely k-trapezoid graphs. To the best of our knowledge, these are the first efficient maximum matching algorithms for trapezoid graphs.

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Counting the number of vertex covers in a trapezoid graph

Cited by 10 publications

References 18 publications

Counting independent sets and its variation in cocomparability graphs

Counting independent sets and its variation in cocomparability graphs

Closest Pair and the Post Office Problem for Stochastic Points

Efficient maximum matching algorithms for trapezoid graphs

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