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Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model

Authors Sharareh Alipour , Ermiya Farokhnejad , Tobias Mömke

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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Theory of computation → Approximation algorithms analysis
Keywords
  • (1,2)-TSP
  • Max-TSP
  • Maximum Path Cover
  • Semi-Streaming Algorithms
  • Approximation Algorithms
  • Graph Algorithms

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Abstract

We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the (1,2)-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on the closely related Maximum Path Cover Problem, which aims to find a collection of vertex-disjoint paths that covers the maximum number of edges in a graph. We propose an algorithm that, for any ε > 0, achieves a (2/3-ε)-approximation of the maximum path cover size for an n-vertex graph, using poly(1/ε) passes. This result improves upon the previous 1/2-approximation by Behnezhad et al. [Soheil Behnezhad et al., 2023] in the semi-streaming model. Building on this result, we design a semi-streaming algorithm that constructs a tour for an instance of (1,2)-TSP with an approximation factor of (4/3 + ε), improving upon the previous 3/2-approximation factor algorithm by Behnezhad et al. [Soheil Behnezhad et al., 2023].
Furthermore, we extend our approach to develop an approximation algorithm for the Maximum TSP (Max-TSP), where the goal is to find a Hamiltonian cycle with the maximum possible weight in a given weighted graph G. Our algorithm provides a (7/12 - ε)-approximation for Max-TSP in poly(1/(ε)) passes, improving on the previously known (1/2-ε)-approximation obtained via maximum weight matching in the semi-streaming model.

Cite As Get BibTex

Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke. Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.9

Author Details

Sharareh Alipour
  • Department of Computer Science, Tehran Institute for Advanced Studies (TeIAS), Khatam University, Tehran, Iran
Ermiya Farokhnejad
  • Department of Computer Science, University of Warwick, Coventry, UK
Tobias Mömke
  • Department of Computer Science, University of Augsburg, Germany

Funding

  • Mömke, Tobias: Partially supported by DFG Grant 439522729 (Heisenberg-Grant).

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