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- W1676390513 abstract "We study algorithms based on local improvements for the (k)-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from (frac{k}{2}+epsilon ) to (frac{k+2}{3}), and by Cygan [7] to (frac{k+1}{3}+epsilon ) for any (epsilon >0). In this paper, we achieve the approximation ratio (frac{k+1}{3}+epsilon ) for the (k)-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in (frac{1}{epsilon ^2}), while the running time of Cygan’s algorithm [7] is doubly exponential in (frac{1}{epsilon }). On the other hand, we construct an instance with locality gap (frac{k+1}{3}) for any algorithm using local improvements of size (O(n^{1/5})), where (n) is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements." @default.
- W1676390513 created "2016-06-24" @default.
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- W1676390513 date "2014-01-01" @default.
- W1676390513 modified "2023-09-23" @default.
- W1676390513 title "Approximating the $$k$$ -Set Packing Problem by Local Improvements" @default.
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- W1676390513 doi "https://doi.org/10.1007/978-3-319-09174-7_35" @default.
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