文章基本信息

标题：Parameterized Complexity of Directed Spanner Problems
本地全文：下载
作者：Fedor V. Fomin ; Petr A. Golovach ; William Lochet 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：180
页码：1-11
DOI：10.4230/LIPIcs.IPEC.2020.12
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most m-k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most m-k arcs. We show that - Directed Multiplicative Spanner admits a polynomial kernel of size ð'ª(kâ´tâµ) and can be solved in randomized (4t)^kâ<. n^ð'ª(1) time, - Directed Additive Spanner is W[1]-hard when parameterized by k even if t = 1 and the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is FPT when parameterized by t and k.
关键词：Graph spanners; directed graphs; parameterized complexity; kernelization