Minsum 2paths problems
Fenner, Trevor and Lachish, Oded and Popa, A. (2016) Minsum 2paths problems. Theory of Computing Systems 58 (1), pp. 94110. ISSN 14324350.

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Abstract
An orientation of an undirected graph G is a directed graph obtained by replacing each edge {u,v} of G by exactly one of the arcs (u,v) or (v,u). In the minsum k paths orientation problem, the input is an undirected graph G and ordered pairs (s i ,t i ), where i∈{1,2,…,k}. The goal is to find an orientation of G that minimizes the sum over all i∈{1,2,…,k} of the distance from s i to t i . In the minsum k edgedisjoint paths problem, the input is the same, however the goal is to find for every i∈{1,2,…,k} a path between s i and t i so that these paths are edgedisjoint and the sum of their lengths is minimum. Note that, for every fixed k≥2, the question of N Phardness for the minsum kpaths orientation problem and for the minsum k edgedisjoint paths problem has been open for more than two decades. We study the complexity of these problems when k=2. We exhibit a PTAS for the minsum 2paths orientation problem. A byproduct of this PTAS is a reduction from the minsum 2paths orientation problem to the minsum 2 edgedisjoint paths problem. The implications of this reduction are: (i) an NPhardness proof for the minsum 2paths orientation problem yields an NPhardness proof for the minsum 2 edgedisjoint paths problem, and (ii) any approximation algorithm for the minsum 2 edgedisjoint paths problem can be used to construct an approximation algorithm for the minsum 2paths orientation problem with the same approximation guarantee and only an additive polynomial increase in the running time.
Metadata
Item Type:  Article 

Additional Information:  The final publication is available at Springer via the link above. 
Keyword(s) / Subject(s):  Graph, Algorithms, Paths, Orientation, Minsum 
School:  Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems 
Depositing User:  Oded Lachish 
Date Deposited:  25 May 2016 13:35 
Last Modified:  21 Apr 2017 10:35 
URI:  http://eprints.bbk.ac.uk/id/eprint/15295 
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