TY - UNPB
T1 - A Brief Note on Single Source Fault Tolerant Reachability.
AU - Lokshtanov, Daniel
AU - Misra, Pranabendu
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2019/4
Y1 - 2019/4
N2 - Let G be a directed graph with n vertices and m edges, and let s∈V(G) be a designated source vertex. We consider the problem of single source reachability (SSR) from s in presence of failures of edges (or vertices). Formally, a spanning subgraph H of G is a {\em k-Fault Tolerant Reachability Subgraph (k-FTRS)} if it has the following property. For any set F of at most k edges (or vertices) in G, and for any vertex v∈V(G), the vertex v is reachable from s in G−F if and only if it is reachable from s in H−F. Baswana this http URL. [STOC 2016, SICOMP 2018] showed that in the setting above, for any positive integer k, we can compute a k-FTRS with 2kn edges. In this paper, we give a much simpler algorithm for computing a k-FTRS, and observe that it extends to higher connectivity as well. Our results follow from a simple application of \emph{important separators}, a well known technique in Parameterized Complexity.
AB - Let G be a directed graph with n vertices and m edges, and let s∈V(G) be a designated source vertex. We consider the problem of single source reachability (SSR) from s in presence of failures of edges (or vertices). Formally, a spanning subgraph H of G is a {\em k-Fault Tolerant Reachability Subgraph (k-FTRS)} if it has the following property. For any set F of at most k edges (or vertices) in G, and for any vertex v∈V(G), the vertex v is reachable from s in G−F if and only if it is reachable from s in H−F. Baswana this http URL. [STOC 2016, SICOMP 2018] showed that in the setting above, for any positive integer k, we can compute a k-FTRS with 2kn edges. In this paper, we give a much simpler algorithm for computing a k-FTRS, and observe that it extends to higher connectivity as well. Our results follow from a simple application of \emph{important separators}, a well known technique in Parameterized Complexity.
U2 - 10.48550/arXiv.1904.08150
DO - 10.48550/arXiv.1904.08150
M3 - Preprint
VL - abs/1904.08150
BT - A Brief Note on Single Source Fault Tolerant Reachability.
PB - arXiv
ER -