Restless Temporal Path Parameterized Above Lower Bounds

03/29/2022
by   Philipp Zschoche, et al.
0

Reachability questions are one of the most fundamental algorithmic primitives in temporal graphs – graphs whose edge set changes over discrete time steps. A core problem here is the NP-hard Short Restless Temporal Path: given a temporal graph 𝒢, two distinct vertices s and z, and two numbers δ and k, is there a δ-restless temporal s-z path of length at most k? A temporal path is a path whose edges appear in chronological order and a temporal path is δ-restless if two consecutive path edges appear at most δ time steps apart from each other. Among others, this problem has applications in neuroscience and epidemiology. While Short Restless Temporal Path is known to be computationally hard, e.g., it is NP-hard for only three time steps and W[1]-hard when parameterized by the feedback vertex number of the underlying graph, it is fixed-parameter tractable when parameterized by the path length k. We improve on this by showing that Short Restless Temporal Path can be solved in (randomized) 4^k-d|𝒢|^O(1) time, where d is the minimum length of a temporal s-z path.

READ FULL TEXT

page 1

page 3

page 13

page 15

research
10/16/2020

Restless reachability problems in temporal graphs

We study a family of reachability problems under waiting-time restrictio...
research
03/31/2022

Finding Balance-Fair Short Paths in Graphs

The computation of short paths in graphs with edge lengths is a pillar o...
research
04/06/2022

Disentangling the Computational Complexity of Network Untangling

We study the network untangling problem introduced by Rozenshtein, Tatti...
research
03/01/2018

Temporal Graph Classes: A View Through Temporal Separators

We investigate the computational complexity of separating two distinct v...
research
11/17/2021

Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring

We consider the algorithmic complexity of recognizing bipartite temporal...
research
05/18/2021

Interference-free Walks in Time: Temporally Disjoint Paths

We investigate the computational complexity of finding temporally disjoi...
research
05/25/2021

On Finding Separators in Temporal Split and Permutation Graphs

Removing all connections between two vertices s and z in a graph by remo...

Please sign up or login with your details

Forgot password? Click here to reset