TY - GEN

T1 - Two moves per time step make a difference

AU - Erlebach, Thomas

AU - Kammer, Frank

AU - Luo, Kelin

AU - Sajenko, Andrej

AU - Spooner, Jakob T.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - A temporal graph is a graph whose edge set can change over time. We only require that the edge set in each time step forms a connected graph. The temporal exploration problem asks for a temporal walk that starts at a given vertex, moves over at most one edge in each time step, visits all vertices, and reaches the last unvisited vertex as early as possible. We show in this paper that every temporal graph with n vertices can be explored in O(n1.75) time steps provided that either the degree of the graph is bounded in each step or the temporal walk is allowed to make two moves per step. This result is interesting because it breaks the lower bound of Ω(n2) steps that holds for the worst-case exploration time if only one move per time step is allowed and the graph in each step can have arbitrary degree. We complement this main result by a logarithmic inapproximability result and a proof that for sparse temporal graphs (i.e., temporal graphs with O(n) edges in the underlying graph) making O(1) moves per time step can improve the worst-case exploration time at most by a constant factor.

AB - A temporal graph is a graph whose edge set can change over time. We only require that the edge set in each time step forms a connected graph. The temporal exploration problem asks for a temporal walk that starts at a given vertex, moves over at most one edge in each time step, visits all vertices, and reaches the last unvisited vertex as early as possible. We show in this paper that every temporal graph with n vertices can be explored in O(n1.75) time steps provided that either the degree of the graph is bounded in each step or the temporal walk is allowed to make two moves per step. This result is interesting because it breaks the lower bound of Ω(n2) steps that holds for the worst-case exploration time if only one move per time step is allowed and the graph in each step can have arbitrary degree. We complement this main result by a logarithmic inapproximability result and a proof that for sparse temporal graphs (i.e., temporal graphs with O(n) edges in the underlying graph) making O(1) moves per time step can improve the worst-case exploration time at most by a constant factor.

KW - Algorithmic Graph Theory

KW - NP-Complete Problem

KW - Temporal Graph Exploration

UR - http://www.scopus.com/inward/record.url?scp=85069178550&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2019.141

DO - 10.4230/LIPIcs.ICALP.2019.141

M3 - Conference contribution

AN - SCOPUS:85069178550

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

A2 - Baier, Christel

A2 - Chatzigiannakis, Ioannis

A2 - Flocchini, Paola

A2 - Leonardi, Stefano

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

T2 - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

Y2 - 9 July 2019 through 12 July 2019

ER -