منابع مشابه
Sparse Hypercube 3-spanners
A t-spanner of a graph G = (V,E), is a sub-graph SG = (V,E′), such that E′ ⊆ E and for every edge (u, v) ∈ E, there is a path from u to v in SG of length at most t. A minimum-edge t-spanner of a graph G, S′ G, is the t-spanner of G with the fewest edges. For general graphs and for t=2, the problem of determining for a given integer s, whether |E(S′ G)| ≤ s is NP-Complete [2]. Peleg and Ullman [...
متن کاملSpanners in Sparse Graphs
A t-spanner of a graph G is a spanning subgraph S in which the distance between every pair of vertices is at most t times their distance in G. If S is required to be a tree then S is called a tree t-spanner of G. In 1998, Fekete and Kremer showed that on unweighted planar graphs the tree t-spanner problem (the problem to decide whether G admits a tree t-spanner) is polynomial time solvable for ...
متن کاملSparse Roadmap Spanners
Asymptotically optimal planners, such as PRM⇤, guarantee that solutions approach optimal as iterations increase. Roadmaps with this property, however, may grow too large. If optimality is relaxed, asymptotically near-optimal solutions produce sparser graphs by not including all edges. The idea stems from graph spanner algorithms, which produce sparse subgraphs that guarantee near-optimal paths....
متن کاملGenerating Sparse 2-spanners
A k?spanner of a connected graph G = (V; E) is a subgraph G 0 consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G 0 is larger than that distance in G by no more than a factor of k. This note concerns the problem of nding the sparsest 2-spanner in a given graph, and presents an approximation algorithm for thi...
متن کاملTransitive-Closure Spanners of the Hypercube and the Hypergrid
Given a directed graph G = (V,E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TCspanner) of G is a directed graph H = (V,EH) that has (1) the same transitive-closure as G and (2) diameter at most k. Transitive-closure spanners were introduced in [7] as a common abstraction for applications in access control, property testing and data structures. In this work we study the number of ed...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2000
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00246-2