Journal ArticleDOI
An optimal algorithm to solve the all‐pair shortest path problem on interval graphs
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An O(n2) time-optimal algorithm for solving the unweighted all-pair shortest path problem on interval graphs, an important subclass of perfect graphs.Abstract:
We present an O(n2) time-optimal algorithm for solving the unweighted all-pair shortest path problem on interval graphs, an important subclass of perfect graphs. An interesting structure called the neighborhood tree is studied and used in the algorithm. This tree is formed by identifying the successive neighborhoods of the vertex labeled last in the graph according to the IG-ordering.read more
Citations
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Journal ArticleDOI
Fast Approximation of Centrality
David Eppstein,Joseph Wang +1 more
TL;DR: A randomized approximation algorithm for centrality in weighted graphs is described that estimates the centrality of all vertices with high probability within a (1 + ∈) factor in near-linear time for graphs exhibiting the small world phenomenon.
Proceedings ArticleDOI
Fast approximation of centrality
David Eppstein,Joseph Wang +1 more
TL;DR: In this paper, a randomized approximation algorithm for centrality in weighted graphs was proposed, which estimates the centrality of all vertices with high probability within a (1 + ∈) factor in nearlinear time.
Journal ArticleDOI
An optimal algorithm for shortest paths on weighted interval and circular-arc graphs, with applications
TL;DR: In this article, a linear-time algorithm for computing single-source shortest paths in a weighted interval or circular-arc graph was given, where n is the number of intervals or circular arcs in a graph.
Journal ArticleDOI
An optimal algorithm for solving all-pairs shortest paths on trapezoid graphs
TL;DR: This paper presents an O(n2) time algorithm for solving all pairs shortest path problems on trapezoid graphs which are extensions of interval graphs and permutation graphs.
Journal ArticleDOI
Estimating all pairs shortest paths in restricted graph families: a unified approach
TL;DR: A very simple and efficient approach can be used to solve the all pairs almost shortest path problem on the class of weakly chordal graphs and its different subclasses and gives a unified way to solve all pairsalmost shortest path problems on different graph classes.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Book
Algorithmic graph theory and perfect graphs
TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.
Journal ArticleDOI
Finding Hamiltonian circuits in interval graphs
TL;DR: This paper presents a linear time algorithm for the Hamiltonian circuit problem in interval graphs and shows that this problem remains NP-complete for planar 3-connected graphs, bipartite graphs, and grid graphs.
Journal ArticleDOI
A unified approach to domination problems on interval graphs
TL;DR: Une propriete tres simple des graphes intervalle is utilisee dans la realisation d'algorithmes a temps lineaire, developpes pour la resolution de differents problemes de domination as mentioned in this paper.
Journal ArticleDOI
The complexity of generalized clique covering
Derek G. Corneil,J. Fonlupt +1 more
TL;DR: It is shown that for i >62; j ≥1 the C i,j problem is NP-complete for arbitrary graphs and a polynomial-time dynamic programming algorithm algorithm is exhibited for the Ci 1 problem on chordal graphs, for i ≥3.