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Dictionary matching and indexing with errors and don't cares
tl;dr
This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly. Expand
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  • Open Access
Uniquely Restricted Matchings
tl;dr
We introduce a new, specialized type of matching which we call uniquely restricted matchings, originally motivated by the problem of determining a lower bound on the rank of a matrix having a specified zero/ non-zero pattern. Expand
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Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
tl;dr
We prove that if the d-regular multigraph does not contain more than ⌊d/2⌋ copies of any 2-cycles then we can find a similar decomposition into n2 pairs of cycle covers where each 2-cycle occurs in at most one component of each pair. Expand
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  • Open Access
Faster algorithms for string matching with k mismatches
tl;dr
The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T. Currently, the fastest algorithms for this problem are the Galil-Giancarlo and Abrahamson algorithms. Expand
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  • Open Access
New results on induced matchings
tl;dr
A matching in a graph is a set of edges no two of which share a common vertex. Expand
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Clustered Integer 3SUM via Additive Combinatorics
tl;dr
We present a collection of new results on problems related to3SUM, including: The first truly subquadratic algorithm for computing the (min,+) convolution for monotone increasing sequences with integer values bounded by O(n), solving 3SUM formonotone sets in 2D with integer coordinates, and preprocessing a binary string for histogram indexing (also called jumbled indexing). Expand
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  • Open Access
Improved algorithms for the k simple shortest paths and the replacement paths problems
tl;dr
We present two simple algorithms for the replacement paths problem and the k simple shortest paths problem in weighted directed graphs (using a solution of the All Pairs Shortest Paths problem). Expand
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Pattern Matching in Hypertext
tl;dr
The importance of hypertext has been steadily growing over the past decade. Expand
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  • Open Access
Longest Common Extensions in Sublinear Space
tl;dr
The longest common extension problem (LCE problem) is to construct a data structure for an input string \(T\) of length \(n\) that supports \({\mathrm {LCE}}(i,j)\) queries. Expand
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  • Open Access
Two-Dimensional Range Minimum Queries
tl;dr
We present a class of algorithms which can solve the 2-dimensional Range Minimum Query-problem with O(kN) additional space, O(N log[k+1] N) preprocessing time and O(1) query time for any k > 1, where log is the iterated application of k + 1 logarithms. Expand
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