eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-30
54:1
54:15
10.4230/LIPIcs.ESA.2023.54
article
Improved Approximation Algorithms for the Expanding Search Problem
Griesbach, Svenja M.
1
https://orcid.org/0000-0001-8018-3289
Hommelsheim, Felix
2
https://orcid.org/0000-0003-4444-9793
Klimm, Max
1
https://orcid.org/0000-0002-9061-2267
Schewior, Kevin
3
https://orcid.org/0000-0003-2236-0210
Institute for Mathematics, Technische Universität Berlin, Germany
Faculty of Mathematics and Computer Science, Universität Bremen, Germany
Department Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark
A searcher faces a graph with edge lengths and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge length. The goal is to minimize the weighted sum of the exploration times over all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the general case, we give a (2e+ε)-approximation for any ε > 0. For the case that all vertices have unit weight, we provide a 2e-approximation. Finally, we provide a PTAS for the case of a Euclidean graph. Previously, for all cases only an 8-approximation was known.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol274-esa2023/LIPIcs.ESA.2023.54/LIPIcs.ESA.2023.54.pdf
Approximation Algorithm
Expanding Search
Search Problem
Graph Exploration
Traveling Repairperson Problem