In the model of local computation algorithms (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with subexponential dependence on d, while maintaining polylogarithmic dependence on n. We present:
-a randomized LCA for computing maximal independent sets whose time and space complexities are quasi-polynomial in d and polylogarithmic in n;
-for constant ε>0, a randomized LCA that provides a (1−ε)-approximation to maximum matching with high probability, whose time and space complexities are polynomial in d and polylogarithmic in n.
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Algorithms and Complexities of Matching Variants in Covariate Balancing
Here, we study several variants of matching problems that arise in covariate balancing. Covariate balancing problems can be viewed as variants of matching, or b-matching, with global side constraints. We present here a comprehensive complexity study of the covariate balancing problems providing polynomial time algorithms, or a proof of NP-hardness. The polynomial time algorithms described are mostly combinatorial and rely on network flow techniques. In addition, we present several fixed-parameter tractable results for problems where the number of covariates and the number of levels of each covariate are seen as a parameter.
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- Award ID(s):
- 1760102
- NSF-PAR ID:
- 10356989
- Date Published:
- Journal Name:
- Operations Research
- ISSN:
- 0030-364X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/opre.2022.2286
