TY - GEN

T1 - The shortest separating cycle problem

AU - Arkin, Esther M.

AU - Gao, Jie

AU - Hesterberg, Adam

AU - Mitchell, Joseph S.B.

AU - Zeng, Jiemin

N1 - Funding Information:
E. Arkin and J. Mitchell acknowledge support from NSF (CCF-1526406). J. Gao and J. Zeng acknowledge support from AFOSR (FA9550-14-1-0193) and NSF (CNS-1217823, DMS-1418255, CCF-1535900).
Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - Given a set of pairs of points in the plane, the goal of the shortest separating cycle problem is to find a simple tour of minimum length that separates the two points of each pair to different sides. In this article we prove hardness of the problem and provide approximation algorithms under various settings. Assuming the Unique Games Conjecture, the problem cannot be approximated within a factor of 2. We provide a polynomial algorithm when all pairs are unit length apart with horizontal orientation inside a square board of size 2 − ε. We provide constant approximation algorithms for unit length horizontal or vertical pairs or constant length pairs on points laying on a grid. For pairs with no restriction we have an O(√n)-approximation algorithm and an O(log n)- approximation algorithm for the shortest separating planar graph.

AB - Given a set of pairs of points in the plane, the goal of the shortest separating cycle problem is to find a simple tour of minimum length that separates the two points of each pair to different sides. In this article we prove hardness of the problem and provide approximation algorithms under various settings. Assuming the Unique Games Conjecture, the problem cannot be approximated within a factor of 2. We provide a polynomial algorithm when all pairs are unit length apart with horizontal orientation inside a square board of size 2 − ε. We provide constant approximation algorithms for unit length horizontal or vertical pairs or constant length pairs on points laying on a grid. For pairs with no restriction we have an O(√n)-approximation algorithm and an O(log n)- approximation algorithm for the shortest separating planar graph.

KW - Shortest separating cycle

KW - Traveling salesman problem

UR - http://www.scopus.com/inward/record.url?scp=85010690607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010690607&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-51741-4_1

DO - 10.1007/978-3-319-51741-4_1

M3 - Conference contribution

AN - SCOPUS:85010690607

SN - 9783319517407

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 13

BT - Approximation and Online Algorithms - 14th International Workshop, WAOA 2016, Revised Selected Papers

A2 - Mastrolilli, Monaldo

A2 - Jansen, Klaus

PB - Springer Verlag

T2 - 14th International Workshop on Approximation and Online Algorithms, WAOA 2016

Y2 - 25 August 2016 through 26 August 2016

ER -