Linear-time string-matching using only a fixed number of local storage locations

Travel-Time Maps: Linear Cartograms with Fixed Vertex Locations

Linear cartograms visualize travel times between locations, usually by deforming the underlying map such that Euclidean distance corresponds to travel time. We introduce an alternative model, where the map and the locations remain fixed, but edges are drawn as sinusoid curves. Now the travel time over a road corresponds to the length of the curve. Of course the curves might intersect if not pla...

Space Complexity of Linear Time Approximate String Matching

Approximate string matching is a sequential problem and therefore it is possible to solve it using nite automata. Nondeterministic nite automata are constructed for string matching with k mismatches and k di erences. The corresponding deterministic nite automata are base for approximate string matching in linear time. Then the space complexity of both types of deterministic automata is calculat...

Sub-string/Pattern Matching in Sub-linear Time Using a Sparse Fourier Transform Approach

We consider the problem of querying a string (or, a database) of length N bits to determine all the locations where a substring (query) of length M appears either exactly or is within a Hamming distance of K from the query. We assume that sketches of the original signal can be computed off line and stored. Using the sparse Fourier transform computation based approach introduced by Pawar and Ram...

A Linear Time Pattern Matching Algorithm Between a String and a Tree

String Matching with Inversions and Translocations in Linear Average Time (Most of the Time)

We present an efficient algorithm for finding all approximate occurrences of a given pattern p of length m in a text t of length n allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm is based on an efficient filtering method and has an O(nmmax(α, β))-time complexity in the worst case and O(max(α, β))space complexity, where α and β are respective...