The k-distinct language: Parameterized automata constructions

Ran Ben-Basat, Ariel Gabizon, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper, we pioneer a study of parameterized automata constructions for languages relevant to the design of parameterized algorithms. We focus on the k-Distinct language Lk(Σ) ⊆ Σk, defined as the set of words of length k whose symbols are all distinct. This language is implicitly related to several breakthrough techniques, developed during the last two decades, to design parameterized algorithms for fundamental problems such as k-Path and r-Dimensional k-Matching. Building upon the well-known color coding, divide-and-color and narrow sieves techniques, we obtain the following automata constructions for Lk(Σ). We develop non-deterministic automata (NFAs) of sizes 4k+o(k)·nO(1) and (2e)k+o(k)·nO(1), where the latter satisfies a ‘bounded ambiguity’ property relevant to approximate counting, as well as a non-deterministic xor automaton (NXA) of size 2k·nO(1), where n = |Σ|.We show that our constructions lead to a unified approach for the design of both deterministic and randomized algorithms for parameterized problems, considering also their approximate counting variants. To demonstrate our approach, we consider the k-Path, r-Dimensional k-Matching and Module Motif problems.

Original languageEnglish
Title of host publicationParameterized and Exact Computation - 9th International Symposium, IPEC 2014, Revised Selected Papers
EditorsMarek Cygan, Pinar Heggernes
PublisherSpringer Verlag
Pages85-96
Number of pages12
ISBN (Electronic)9783319135236
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes
Event9th International Symposium on Parameterized and Exact Computation, IPEC 2014 - Wroclaw, Poland
Duration: 10 Sep 201412 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8894
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th International Symposium on Parameterized and Exact Computation, IPEC 2014
Country/TerritoryPoland
CityWroclaw
Period10/09/1412/09/14

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