Combinatorial Pattern Matching: 17th Annual Symposium, CPM by Amihood Amir (auth.), Moshe Lewenstein, Gabriel Valiente PDF

By Amihood Amir (auth.), Moshe Lewenstein, Gabriel Valiente (eds.)

This e-book constitutes the refereed lawsuits of the seventeenth Annual Symposium on Combinatorial development Matching, CPM 2006, held in Barcelona, Spain in July 2006.

The 33 revised complete papers awarded including three invited talks have been conscientiously reviewed and chosen from 88 submissions. The papers are prepared in topical sections on facts buildings, indexing information constructions, probabilistic and algebraic recommendations, functions in molecular biology, string matching, info compression, and dynamic programming.

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Extra resources for Combinatorial Pattern Matching: 17th Annual Symposium, CPM 2006, Barcelona, Spain, July 5-7, 2006. Proceedings

Sample text

Consider a set of objects [n] and a set of labels [σ], associated in t pairs from [n] × [σ], and a conjunctive query Q composed of k labels from [σ]. There is a deterministic algorithm solving Q in time O(δk lg lg σ), where δ is the minimum number of operations performed by any non-deterministic algorithm to check the result of Q. Proof (sketch). 3] proposed a deterministic algorithm for the conjunctive query that uses O(δk) doubling searches. We replace the doubling search by a combination of label rank, label select and label access operators, and the result follows.

The paper then shows that rmqA (i, j) = E[±1rmqH (R[i], R[j])]. , H has size n := 2n − 1. We now sketch the solution to the ±1RMQ-problem. 4 Define two 2n arrays A and B of size log n , where A [i] stores the minimum of the ith block in H, and B[i] stores the position of this minimum in H. Now A is prepro2n 2n cessed using the algorithm from Sect. 1, occupying O( log n log log n ) = O(n) space. , queries that span over several blocks) to be answered in O(1). It remains to show how in-blockqueries are handled.

We say that COLUMNS is divided into σ parts by ROWS. See the following example: ⎛ ⎞ 0100 ⎜1 1 1 0⎟ ⎟ COLUMNS= 2, 1, 2, 3, 1, 4, 2 M =⎜ ⎝1 0 0 1⎠ ROWS = 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1 0100 1 Row-major order lists the elements from the first row, then from the second row, and so on. 28 J. Barbay et al. We encode COLUMNS using one of the two encodings from Golynski et al [9] depending on the preferred time tradeoffs between different operators as mentioned in the statement of the theorem. These encodings use tM (lg σ + o(lg σ)) bits of space with the following time tradeoffs: string access string select string rank select encoding O(lg lg σ) O(1) O(lg lg σ) access encoding O(1) O(lg lg σ) O(lg lg σ lg lg lg σ) The vector ROWS can be encoded using any succinct fully indexable dictionary that supports in constant time the operators bin rank and bin select, the rank and select operators on binary strings introduced by Jacobson [10] and improved by Clark and Munro [4].

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