Fixed-parameter algorithms for Fair Hitting Set problems
Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a fair version of Hitting Set. In the classical Hitting Set problem, the input is a universe U, a family F of subsets of...
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| Vydáno v: | Information and computation Ročník 302; s. 105261 |
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01.01.2025
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| Abstract | Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a fair version of Hitting Set. In the classical Hitting Set problem, the input is a universe U, a family F of subsets of U, and a non-negative integer k. The goal is to determine whether there exists a subset S⊆U of size k that hits (i.e., intersects) every set in F. Inspired by several recent works, we formulate a fair version of this problem, as follows. The input additionally contains a family B of subsets of U, where each subset in B can be thought of as the group of elements of the same type. We want to find a set S⊆U of size k that (i) hits all sets of F, and (ii) does not contain too many elements of each type. We call this problem Fair Hitting Set, and chart out its tractability boundary from both classical as well as multivariate perspective. Our results use a multitude of techniques from parameterized complexity including classical to advanced tools, such as, methods of representative sets for matroids, FO model checking, and a generalization of best known kernel for Hitting Set. |
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| AbstractList | Selection of a group of representatives satisfying certain fairness constraints, is a commonly occurring scenario. Motivated by this, we initiate a systematic algorithmic study of a fair version of Hitting Set. In the classical Hitting Set problem, the input is a universe U, a family F of subsets of U, and a non-negative integer k. The goal is to determine whether there exists a subset S⊆U of size k that hits (i.e., intersects) every set in F. Inspired by several recent works, we formulate a fair version of this problem, as follows. The input additionally contains a family B of subsets of U, where each subset in B can be thought of as the group of elements of the same type. We want to find a set S⊆U of size k that (i) hits all sets of F, and (ii) does not contain too many elements of each type. We call this problem Fair Hitting Set, and chart out its tractability boundary from both classical as well as multivariate perspective. Our results use a multitude of techniques from parameterized complexity including classical to advanced tools, such as, methods of representative sets for matroids, FO model checking, and a generalization of best known kernel for Hitting Set. |
| ArticleNumber | 105261 |
| Author | Kanesh, Lawqueen Inamdar, Tanmay Purohit, Nidhi Kundu, Madhumita Saurabh, Saket |
| Author_xml | – sequence: 1 givenname: Tanmay orcidid: 0000-0002-0184-5932 surname: Inamdar fullname: Inamdar, Tanmay email: taninamdar@gmail.com organization: Indian Institute of Technology, Jodhpur, Jodhpur, 342030, India – sequence: 2 givenname: Lawqueen surname: Kanesh fullname: Kanesh, Lawqueen email: lawqueen@iitj.ac.in organization: Indian Institute of Technology, Jodhpur, Jodhpur, 342030, India – sequence: 3 givenname: Madhumita surname: Kundu fullname: Kundu, Madhumita email: Madhumita.Kundu@uib.no organization: University of Bergen, Bergen, 5008, Norway – sequence: 4 givenname: Nidhi surname: Purohit fullname: Purohit, Nidhi email: nidhipurohit95@gmail.com organization: Institute of Mathematical Sciences, Chennai, 600113, India – sequence: 5 givenname: Saket surname: Saurabh fullname: Saurabh, Saket email: saket@imsc.res.in organization: University of Bergen, Bergen, 5008, Norway |
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| Cites_doi | 10.1145/3051095 10.1007/s004530010020 10.1016/j.tcs.2009.07.027 10.1016/j.dam.2019.06.001 10.1145/2886094 10.1145/3170444 10.1007/978-3-031-43380-1_1 10.1145/3379698 10.1109/12.24280 10.1007/s00224-019-09964-6 |
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| SubjectTerms | Fairness Hitting set Parameterized complexity |
| Title | Fixed-parameter algorithms for Fair Hitting Set problems |
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