Ayelet Butman

Real scaled matching

Scaled matching refers to the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary integral scale, appears. Scaled matching is an important problem that was originally inspired by problems in Vision. However, in real life, a more natural model of scaled matching is the real scaled matching model. Real scaled matching is an extended version of the scaled matching problem allowing arbitrary real-sized scales, approximated by some function, e.g., truncation. It has been shown that the scaled matching problem can be solved in linear time. However, even though there has been follow-up work on the problem, it remained an open question whether real scaled matching could be solved faster than the simple solution of O(nm) time, where n is the text size and m is the pattern size. Using a new approach we show how to solve the real scaled matching problem in linear time.

Scaled and permuted string matching

The goal of scaled permuted string matching is to find all occurrences of a pattern in a text, in all possible scales and permutations. Given a text of length n and a pattern of length m we present an O(n) algorithm.

Real Two Dimensional Scaled Matching

Scaled Matching refers to the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Scaled matching is an important problem that was originally inspired by Computer Vision.

Two-dimensional pattern matching with rotations

The problem of pattern matching with rotation is that of finding all occurrences of a two-dimensional pattern in a text, in all possible rotations. We prove an upper and lower bound on the number of such different possible rotated patterns. Subsequently, given an m × m array (pattern) and an n × n array (text) over some finite alphabet Σ, we present a new method yielding an O(n2m3) time algorithm for this problem.

Efficient one-dimensional real scaled matching

Real Scaled Matching is the problem of finding all locations in the text where the pattern, proportionally enlarged according to an arbitrary real-sized scale, appears. Real scaled matching is an important problem that was originally inspired by Computer Vision. In this paper, we present a new, more precise and realistic, definition for one-dimensional real scaled matching, and an efficient algorithm for solving this problem. For a text of length n and a pattern of length m, the algorithm runs in time O(nlogm+nm^3^/^2logm).

On the relationship between histogram indexing and block-mass indexing

Histogram indexing, also known as jumbled pattern indexing and permutation indexing is one of the important current open problems in pattern matching. It was introduced about 6 years ago and has seen active research since. Yet, to date there is no algorithm that can preprocess a text T in time o(|T|2/polylog|T|) and achieve histogram indexing, even over a binary alphabet, in time independent of the text length. The pattern matching version of this problem has a simple linear-time solution. Block-mass pattern matching problem is a recently introduced problem, motivated by issues in mass-spectrometry. It is also an example of a pattern matching problem that has an efficient, almost linear-time solution but whose indexing version is daunting. However, for fixed finite alphabets, there has been progress made. In this paper, a strong connection between the histogram indexing problem and the block-mass pattern indexing problem is shown. The reduction we show between the two problems is amazingly simple. Its value lies in recognizing the connection between these two apparently disparate problems, rather than the complexity of the reduction. In addition, we show that for both these problems, even over unbounded alphabets, there are algorithms that preprocess a text T in time o(|T|2/polylog|T|) and enable answering indexing queries in time polynomial in the query length. The contributions of this paper are twofold: (i) we introduce the idea of allowing a trade-off between the preprocessing time and query time of various indexing problems that have been stumbling blocks in the literature. (ii) We take the first step in introducing a class of indexing problems that, we believe, cannot be pre-processed in time o(|T|2/polylog|T|) and enable linear-time query processing.

Pattern matching under polynomial transformation

We consider a class of pattern matching problems where a normalizing polynomial transformation can be applied at every alignment of the pattern and text. Normalized pattern matching plays a key role in fields as diverse as image processing and musical information processing, where application specific transformations are often applied to the input. By considering a wide range of such transformations, we provide fast algorithms and the first lower bounds for both new and old problems. Given a pattern of length

Permuted Scaled Matching

m

Jump-matching with errors

and a longer text of length

Efficient One Dimensional Real Scaled Matching

n