Designing deterministic polynomial-space algorithms by color-coding multivariate polynomials

Gregory Gutin, Felix Reidl, Magnus Wahlström, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 polynomial-space O(3.86k)-time (exponential-space O(3.41k)-time) deterministic algorithm for k-INTERNAL OUT-BRANCHING, improving upon the previously fastest exponential-space O(5.14k)-time algorithm for this problem. (The notation O hides polynomial factors.) We also design polynomial-space O((2e)k+o(k))-time (exponential-space O(4.32k)-time) deterministic algorithms for k-COLORFUL OUT-BRANCHING on arc-colored digraphs and k-COLORFUL PERFECT MATCHING on planar edge-colored graphs. In k-COLORFUL OUT-BRANCHING, given an arc-colored digraph D, decide whether D has an out-branching with arcs of at least k colors. k-COLORFUL PERFECT MATCHING is defined similarly. To obtain our polynomial-space algorithms, we show that (n,k,αk)-splitters (α⩾1) and in particular (n,k)-perfect hash families can be enumerated one by one with polynomial delay using polynomial space.

Original languageEnglish
Pages (from-to)69-85
Number of pages17
JournalJournal of Computer and System Sciences
Volume95
DOIs
StatePublished - 1 Aug 2018
Externally publishedYes

Keywords

  • Deterministic
  • Fixed-parameter tractable
  • Kirchoff matrices
  • Pfaffians
  • Polynomial space

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