Improved Approximation Algorithms for the Expanding Search Problem
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.
Approximation Algorithm
Expanding Search
Search Problem
Graph Exploration
Traveling Repairperson Problem
Theory of computation~Approximation algorithms analysis
54:1-54:15
Regular Paper
https://arxiv.org/abs/2301.03638
We thank Spyros Angelopoulos for fruitful discussions and pointers to earlier literature.
Svenja M.
Griesbach
Svenja M. Griesbach
Institute for Mathematics, Technische Universität Berlin, Germany
https://orcid.org/0000-0001-8018-3289
Supported by Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy, Berlin Mathematics Research Center (grant EXC-2046/1, Project 39068689) and HYPATIA.SCIENCE (Department of Mathematics and Computer Science, University of Cologne).
Felix
Hommelsheim
Felix Hommelsheim
Faculty of Mathematics and Computer Science, Universität Bremen, Germany
https://orcid.org/0000-0003-4444-9793
Max
Klimm
Max Klimm
Institute for Mathematics, Technische Universität Berlin, Germany
https://orcid.org/0000-0002-9061-2267
Supported by Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy, Berlin Mathematics Research Center (grant EXC-2046/1, Project 390685689).
Kevin
Schewior
Kevin Schewior
Department Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark
https://orcid.org/0000-0003-2236-0210
Supported in part by the Independent Research Fund Denmark, Natural Sciences (grant DFF-0135-00018B).
10.4230/LIPIcs.ESA.2023.54
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Svenja M. Griesbach, Felix Hommelsheim, Max Klimm, and Kevin Schewior
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