Temporal cliques admit sparse spanners
نویسندگان
چکیده
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 کاملLower Bound for Sparse Geometric Spanners
Given a one-dimensional graph G such that any two consecutive nodes are unit distance away, and that the minimum number of links between any two nodes (the diameter of G) is O(log n), we provide an Ω(n log n/ log log n) lower bound on the sum of lengths of all the edges (i.e., the weight of G). The problem is a variant of the widely studied partial sums problem. This in turn provides a lower bo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2021
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2021.04.004