research-article

Finding witnesses by peeling

Authors:

Yonatan Aumann,

Moshe Lewenstein,

Noa Lewenstein,

Dekel TsurAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 7, Issue 2

Article No.: 24, Pages 1 - 15

https://doi.org/10.1145/1921659.1921670

Published: 31 March 2011 Publication History

Abstract

In the k-matches problem, we are given a pattern and a text, and for each text location, the desired output consists of all aligned matching characters if there are k or fewer of them, and any k aligned matching characters if there are more than k of them. This problem is one of several string matching problems that seek not only to find where the pattern matches the text under different “match” definitions, but also to provide witnesses to the match. Other such problems include k-aligned ones, k-witnesses, and k-mismatches. In addition, the solutions to several other string matching problems rely on the efficient solutions of the witness finding problems.

In this article we provide a general method for solving such witness finding problems efficiently. We do so by casting the problem as a generalization of group testing, which we then solve by a process we call peeling. Using this general framework we obtain improved results for all of the problems mentioned. We also show that our method also solves a couple of problems outside the pattern matching domain.

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Cited By

Antonopoulos APagourtzis APetsalakis SVasilakis M(2023)Faster algorithms for k-subset sum and variationsJournal of Combinatorial Optimization10.1007/s10878-022-00928-045:1Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1007/s10878-022-00928-0
Antonopoulos APagourtzis APetsalakis SVasilakis M(2022)Faster Algorithms for $$k\text {-}\textsc {Subset}\,\textsc {Sum}$$ and VariationsFrontiers of Algorithmics10.1007/978-3-030-97099-4_3(37-52)Online publication date: 3-Mar-2022
https://doi.org/10.1007/978-3-030-97099-4_3
Koiliaris KXu C(2019)Faster Pseudopolynomial Time Algorithms for Subset SumACM Transactions on Algorithms10.1145/332986315:3(1-20)Online publication date: 12-Jun-2019
https://dl.acm.org/doi/10.1145/3329863
Show More Cited By

Index Terms

Finding witnesses by peeling
1. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Pattern matching
  2. Randomness, geometry and discrete structures

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Two equal-length strings, or two equal-sized two-dimensional texts, parameterize match (p-match) if there is a one-one mapping (relative to the alphabet) of their characters. Two-dimensional parameterized matching is the task of finding all m × m ...

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 7, Issue 2

March 2011

284 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1921659

Issue’s Table of Contents

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 March 2011

Accepted: 01 March 2010

Revised: 01 March 2010

Received: 01 April 2008

Published in TALG Volume 7, Issue 2

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Cited By

Antonopoulos APagourtzis APetsalakis SVasilakis M(2023)Faster algorithms for k-subset sum and variationsJournal of Combinatorial Optimization10.1007/s10878-022-00928-045:1Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1007/s10878-022-00928-0
Antonopoulos APagourtzis APetsalakis SVasilakis M(2022)Faster Algorithms for $$k\text {-}\textsc {Subset}\,\textsc {Sum}$$ and VariationsFrontiers of Algorithmics10.1007/978-3-030-97099-4_3(37-52)Online publication date: 3-Mar-2022
https://doi.org/10.1007/978-3-030-97099-4_3
Koiliaris KXu C(2019)Faster Pseudopolynomial Time Algorithms for Subset SumACM Transactions on Algorithms10.1145/332986315:3(1-20)Online publication date: 12-Jun-2019
https://dl.acm.org/doi/10.1145/3329863
Koiliaris KXu CKlein P(2017)A faster pseudopolynomial time algorithm for subset sumProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039754(1062-1072)Online publication date: 16-Jan-2017
https://dl.acm.org/doi/10.5555/3039686.3039754
Cole RHazay CLewenstein MTsur D(2014)Two-Dimensional Parameterized MatchingACM Transactions on Algorithms10.1145/265022011:2(1-30)Online publication date: 30-Oct-2014
https://dl.acm.org/doi/10.1145/2650220
Björklund APagh RWilliams VZwick U(2014)Listing TrianglesAutomata, Languages, and Programming10.1007/978-3-662-43948-7_19(223-234)Online publication date: 2014
https://doi.org/10.1007/978-3-662-43948-7_19

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