Improved string matching with k mismatches
ACM SIGACT News
Efficient string matching with k mismatches
Theoretical Computer Science
SIAM Journal on Computing
Parallel (PRAM EREW) algorithms for contour-based 2D shape recognition
Pattern Recognition
Efficient 2-dimensional approximate matching of half-rectangular figures
Information and Computation
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Randomized group testing for mutually obscuring defectives
Information Processing Letters
Interpolation of symmetric functions and a new type of combinatorial design
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Selective families, superimposed codes, and broadcasting on unknown radio networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Explicit constructions of selectors and related combinatorial structures, with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Deterministic broadcasting in ad hoc radio networks
Distributed Computing
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
Simple deterministic wildcard matching
Information Processing Letters
Witnesses for Boolean matrix multiplication and for shortest paths
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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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.