TY - GEN
T1 - Neighborhood Persistency of the Linear Optimization Relaxation of Integer Linear Optimization
AU - Kimura, Kei
AU - Nakayama, Kotaro
N1 - Funding Information:
The first author is partially supported by JST, ACT-X Grant Number JPMJAX200C, Japan, and JSPS KAKENHI Grant Numbers JP19K22841, JP21K17700.
Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - For an integer linear optimization (ILO) problem, persistency of its linear optimization (LO) relaxation is a property that for every optimal solution of the relaxation that assigns integer values to some variables, there exists an optimal solution of the ILO problem in which these variables retain the same values. Although persistency has been used to develop heuristic, approximation, and fixed-parameter algorithms for special cases of ILO, its applicability remains unknown in the literature. In this paper, we propose a stronger property called neighborhood persistency and show that the LO relaxation of ILO on unit-two-variable-per-inequality (UTVPI) systems is a maximal class of ILO such that its LO relaxation has (neighborhood) persistency. Our result on neighborhood persistency generalizes the previous results of Nemhauser and Trotter, Hochbaum et al., and Fiorini et al., and implies fixed-parameter tractability and two-approximability for ILO on UTVPI systems where the objective function and the variables are non-negative.
AB - For an integer linear optimization (ILO) problem, persistency of its linear optimization (LO) relaxation is a property that for every optimal solution of the relaxation that assigns integer values to some variables, there exists an optimal solution of the ILO problem in which these variables retain the same values. Although persistency has been used to develop heuristic, approximation, and fixed-parameter algorithms for special cases of ILO, its applicability remains unknown in the literature. In this paper, we propose a stronger property called neighborhood persistency and show that the LO relaxation of ILO on unit-two-variable-per-inequality (UTVPI) systems is a maximal class of ILO such that its LO relaxation has (neighborhood) persistency. Our result on neighborhood persistency generalizes the previous results of Nemhauser and Trotter, Hochbaum et al., and Fiorini et al., and implies fixed-parameter tractability and two-approximability for ILO on UTVPI systems where the objective function and the variables are non-negative.
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U2 - 10.1007/978-3-031-18530-4_23
DO - 10.1007/978-3-031-18530-4_23
M3 - Conference contribution
AN - SCOPUS:85145263137
SN - 9783031185298
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 312
EP - 323
BT - Combinatorial Optimization - 7th International Symposium, ISCO 2022, Revised Selected Papers
A2 - Ljubić, Ivana
A2 - Barahona, Francisco
A2 - Dey, Santanu S.
A2 - Mahjoub, A. Ridha
PB - Springer Science and Business Media Deutschland GmbH
T2 - 7th International Symposium on Combinatorial Optimization, ISCO 2022
Y2 - 18 May 2022 through 20 May 2022
ER -