conference paper
The power of linear programming for finite-valued CSPs: A constructive characterization
LNCS
published
yes
Vladimir
Kolmogorov
author 3D50B0BA-F248-11E8-B48F-1D18A9856A87
VlKo
department
ICALP: Automata, Languages and Programming
A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BLP). Thapper and Živný showed [20] that if BLP solves the language then the language admits a binary commutative fractional polymorphism. We prove that the converse is also true. This leads to a necessary and a sufficient condition which can be checked in polynomial time for a given language. In contrast, the previous necessary and sufficient condition due to [20] involved infinitely many inequalities. More recently, Thapper and Živný [21] showed (using, in particular, a technique introduced in this paper) that core languages that do not satisfy our condition are NP-hard. Taken together, these results imply that a finite-valued language can either be solved using Linear Programming or is NP-hard.
Springer2013Riga, Latvia
eng
1207.721310.1007/978-3-642-39206-1_53
79651625 - 636
https://research-explorer.app.ist.ac.at/record/2271
Kolmogorov, Vladimir. “The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization,” 7965:625–36. Springer, 2013. <a href="https://doi.org/10.1007/978-3-642-39206-1_53">https://doi.org/10.1007/978-3-642-39206-1_53</a>.
V. Kolmogorov, in:, Springer, 2013, pp. 625–636.
Kolmogorov, Vladimir. <i>The Power of Linear Programming for Finite-Valued CSPs: A Constructive Characterization</i>. Vol. 7965, no. 1, Springer, 2013, pp. 625–36, doi:<a href="https://doi.org/10.1007/978-3-642-39206-1_53">10.1007/978-3-642-39206-1_53</a>.
Kolmogorov, V. (2013). The power of linear programming for finite-valued CSPs: A constructive characterization (Vol. 7965, pp. 625–636). Presented at the ICALP: Automata, Languages and Programming, Riga, Latvia: Springer. <a href="https://doi.org/10.1007/978-3-642-39206-1_53">https://doi.org/10.1007/978-3-642-39206-1_53</a>
Kolmogorov V. 2013. The power of linear programming for finite-valued CSPs: A constructive characterization. ICALP: Automata, Languages and Programming, LNCS, vol. 7965, 625–636.
V. Kolmogorov, “The power of linear programming for finite-valued CSPs: A constructive characterization,” presented at the ICALP: Automata, Languages and Programming, Riga, Latvia, 2013, vol. 7965, no. 1, pp. 625–636.
Kolmogorov V. The power of linear programming for finite-valued CSPs: A constructive characterization. In: Vol 7965. Springer; 2013:625-636. doi:<a href="https://doi.org/10.1007/978-3-642-39206-1_53">10.1007/978-3-642-39206-1_53</a>
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