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- W4301785514 abstract "Given an instance I of an optimization constraint satisfaction problem (CSP), finding solutions with value at least the expected value of a random solution is easy. We wonder how good such solutions can be. Namely, we initiate the study of ratio $$rho _E(I) =(mathrm {E}_X[v(I, X)] -mathrm {wor}(I))/(mathrm {opt}(I) -mathrm {wor}(I))$$ where $$mathrm {opt}(I)$$ , $$mathrm {wor}(I)$$ and $$mathrm {E}_X[v(I, X)]$$ refer to respectively the optimal, the worst, and the average solution values on I. We here focus on the case when the variables have a domain of size $$q ge 2$$ and the constraint arity is at most $$k ge 2$$ , where k, q are two constant integers. Connecting this ratio to the highest frequency in orthogonal arrays with specified parameters, we prove that it is $$varOmega (1/n^{k/2})$$ if $$q =2$$ , $$varOmega (1/n^{k -1 -lfloor log _{p^kappa } (k -1)rfloor })$$ where $$p^kappa $$ is the smallest prime power such that $$p^kappa ge q$$ otherwise, and $$varOmega (1/q^k)$$ in $$(max {q, k} +1})$$ -partite instances." @default.
- W4301785514 created "2022-10-05" @default.
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- W4301785514 date "2018-01-01" @default.
- W4301785514 modified "2023-09-23" @default.
- W4301785514 title "How Far From a Worst Solution a Random Solution of a $$k,$$CSP Instance Can Be?" @default.
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- W4301785514 doi "https://doi.org/10.1007/978-3-319-94667-2_31" @default.
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