Approximation algorithms for the total dominating set problem

Limin Wang (), Zhao Zhang (), Donglei Du (), Yaping Mao () and Xiaoyan Zhang ()
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Limin Wang: Henan Institute of Science and Technology
Zhao Zhang: Zhejiang Normal University
Donglei Du: University of New Brunswick
Yaping Mao: Qinghai Normal University
Xiaoyan Zhang: Nanjing Normal University

Journal of Combinatorial Optimization, 2025, vol. 49, issue 5, No 22, 15 pages

Abstract: Abstract Given a network graph $$G=(V,E)$$ G = ( V , E ) , a subset $$T\subseteq V$$ T ⊆ V is said to be a total dominating set (TDS) if every $$v\in V$$ v ∈ V is adjacent to at least one node in T. In this paper, we first present a distributed algorithm for the minimum TDS problem via the LP relaxation techniques. For a positive integer k and maximum degree $$\Delta $$ Δ , the proposed algorithm outputs a fractional total dominating set of expected size $$O(k\Delta ^\frac{2}{k})|TDS_{OPT}|$$ O ( k Δ 2 k ) | T D S OPT | , where $$TDS_{OPT}$$ T D S OPT is an optimal TDS. The distributed algorithm runs in $$O(k^2)$$ O ( k 2 ) communication rounds, and the algorithm uses messages of size $$O(\log \Delta )$$ O ( log Δ ) . Then we give a rounding algorithm. The fractional solution is rounded to obtain an integer total dominating set for the original problem.

Keywords: Total dominating set; Distributed; Approximation algorithm; Rounding algorithm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01311-5

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