A $$(1.4 + \epsilon )$$ ( 1.4 + ϵ ) -approximation algorithm for the 2-Max-Duo problem

Yong Chen (), Guohui Lin (), Tian Liu (), Taibo Luo (), Bing Su (), Yao Xu () and Peng Zhang ()
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Yong Chen: Hangzhou Dianzi University
Guohui Lin: University of Alberta
Tian Liu: Peking University
Taibo Luo: Xidian University
Bing Su: Xi’an Technological University
Yao Xu: Kettering University
Peng Zhang: Shandong University

Journal of Combinatorial Optimization, 2020, vol. 40, issue 3, No 12, 806-824

Abstract: Abstract The maximum duo-preservation string mapping (Max-Duo) problem is the complement of the well studied minimum common string partition problem, both of which have applications in many fields including text compression and bioinformatics. k-Max-Duo is the restricted version of Max-Duo, where every letter of the alphabet occurs at most k times in each of the strings, which is readily reduced into the well known maximum independent set (MIS) problem on a graph of maximum degree $$\Delta \le 6(k-1)$$ Δ ≤ 6 ( k - 1 ) . In particular, 2-Max-Duo can then be approximated arbitrarily close to 1.8 using the state-of-the-art approximation algorithm for the MIS problem on bounded-degree graphs. 2-Max-Duo was proved APX-hard and very recently a $$(1.6 + \epsilon )$$ ( 1.6 + ϵ ) -approximation algorithm was claimed, for any $$\epsilon > 0$$ ϵ > 0 . In this paper, we present a vertex-degree reduction technique, based on which, we show that 2-Max-Duo can be approximated arbitrarily close to 1.4.

Keywords: Approximation algorithm; Duo-preservation string mapping; String partition; Independent set; F.2.2 Pattern matching; G.2.1 Combinatorial algorithms; G.4 Algorithm design and analysis (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-020-00621-0

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