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- W4300889628 abstract "In recent years, several powerful techniques have been developed to design {em randomized} polynomial-space parameterized algorithms. In this paper, we introduce an enhancement of color coding to design deterministic polynomial-space parameterized algorithms. Our approach aims at reducing the number of random choices by exploiting the special structure of a solution. Using our approach, we derive the following deterministic algorithms (see Introduction for problem definitions). 1. Polynomial-space $O^*(3.86^k)$-time (exponential-space $O^*(3.41^k)$-time) algorithm for {sc $k$-Internal Out-Branching}, improving upon the previously fastest {em exponential-space} $O^*(5.14^k)$-time algorithm for this problem. 2. Polynomial-space $O^*((2e)^{k+o(k)})$-time (exponential-space $O^*(4.32^k)$-time) algorithm for {sc $k$-Colorful Out-Branching} on arc-colored digraphs and {sc $k$-Colorful Perfect Matching} on planar edge-colored graphs. To obtain our polynomial space algorithms, we show that $(n,k,alpha k)$-splitters ($alphage 1$) and in particular $(n,k)$-perfect hash families can be enumerated one by one with polynomial delay." @default.
- W4300889628 created "2022-10-04" @default.
- W4300889628 creator A5001475076 @default.
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- W4300889628 date "2017-06-12" @default.
- W4300889628 modified "2023-09-26" @default.
- W4300889628 title "Designing Deterministic Polynomial-Space Algorithms by Color-Coding Multivariate Polynomials" @default.
- W4300889628 doi "https://doi.org/10.48550/arxiv.1706.03698" @default.
- W4300889628 hasPublicationYear "2017" @default.
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