TY - JOUR

T1 - NP-hardness of two edge cover generalizations with applications to control and bribery for approval voting

AU - Bredereck, Robert

AU - Talmon, Nimrod

N1 - Funding Information:
We are grateful to the anonymous referees of Information Processing Letters whose comments helped us to improve this paper. Robert Bredereck was supported by the DFG , project PAWS ( NI 369/10 ). Nimrod Talmon was supported by DFG Research Training Group “Methods for Discrete Structures” ( GRK 1408 ).
Publisher Copyright:
© 2015 Elsevier B.V.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - Given an undirected graph and an integer q, the Edge Cover problem asks for a subgraph with at most q edges such that each vertex has degree at least one. We show NP-hardness of two generalizations of the Edge Cover problem, which were conjectured to be polynomial-time solvable, solving three open questions from computational social choice. Both generalizations introduce weights on the edges and an individual demand b(v) for each vertex v. The first generalization, named Simple b-Edge Weighted Cover, requires the edge set to have a total weight of at most q while each vertex v is to be adjacent to at least b(v) edges. The second generalization, named Simple Weighted b-Edge Cover, requires the edge set to contain at most q edges while each vertex v is to be adjacent to edges of total weight at least b(v).

AB - Given an undirected graph and an integer q, the Edge Cover problem asks for a subgraph with at most q edges such that each vertex has degree at least one. We show NP-hardness of two generalizations of the Edge Cover problem, which were conjectured to be polynomial-time solvable, solving three open questions from computational social choice. Both generalizations introduce weights on the edges and an individual demand b(v) for each vertex v. The first generalization, named Simple b-Edge Weighted Cover, requires the edge set to have a total weight of at most q while each vertex v is to be adjacent to at least b(v) edges. The second generalization, named Simple Weighted b-Edge Cover, requires the edge set to contain at most q edges while each vertex v is to be adjacent to edges of total weight at least b(v).

KW - Approval voting

KW - Computational complexity

KW - Computational social choice

KW - Graph problems

KW - Manipulating elections

UR - http://www.scopus.com/inward/record.url?scp=84948799763&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2015.09.008

DO - 10.1016/j.ipl.2015.09.008

M3 - Article

AN - SCOPUS:84948799763

SN - 0020-0190

VL - 116

SP - 147

EP - 152

JO - Information Processing Letters

JF - Information Processing Letters

IS - 2

ER -