nan Diptarama

Computing Longest Single-arm-gapped Palindromes in a String

We introduce new types of approximate palindromes called single-arm-gapped palindromes (SAGPs). A SAGP contains a gap in either its left or right arm, which is in the form of either \(wguc u^R w^R\) or \(wuc u^Rgw^R\), where w and u are non-empty strings, \(w^R\) and \(u^R\) are their reversed strings respectively, g is a gap, and c is either a single character or the empty string. We classify SAGPs into two groups: those which have \(ucu^R\) as a maximal palindrome (type-1), and the others (type-2). We propose several algorithms to compute all type-1 SAGPs with longest arms occurring in a given string using suffix arrays, and them a linear-time algorithm based on suffix trees. We also show how to compute type-2 SAGPs with longest arms in linear time. We perform some preliminary experiments to evaluate practical performances of the proposed methods.

Longest Common Subsequence in at Least k Length Order-Isomorphic Substrings

We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least k length substrings. First, we show an O(mn) time algorithm for the problem which gives a better worst-case running time than existing algorithms, where m and n are lengths of the input strings. Furthermore, we mainly consider the LCS in at least k length order-isomorphic substrings problem. We show that the problem can also be solved in O(mn) worst-case time by an easy-to-implement algorithm.

AC-Automaton Update Algorithm for Semi-dynamic Dictionary Matching

Given a set of pattern strings called a dictionary and a text string, dictionary matching is the problem to find the occurrences of the patterns on the text. Dynamic dictionary matching is dictionary matching where patterns may dynamically be inserted into and deleted from the dictionary. The problem is called semi-dynamic dictionary matching when we only consider the insertion. An AC-automaton is a data structure which enables us to solve dictionary matching in \(O(d\log \sigma )\) preprocessing time and \(O(n\log \sigma )\) matching time, where d denotes the total length of the patterns in the dictionary, n denotes the length of the text, and \(\sigma \) denotes the alphabet size. In this paper we propose an efficient algorithm that dynamically updates an AC automaton for insertion of a new pattern by using a directed acyclic word graph.

New Variants of Pattern Matching with Constants and Variables.

Given a text and a pattern over two types of symbols called constants and variables, the parameterized pattern matching problem is to find all occurrences of substrings of the text that the pattern matches by substituting a variable in the text for each variable in the pattern, where the substitution should be injective. The function matching problem is a variant of it that lifts the injection constraint. In this paper, we discuss variants of those problems, where one can substitute a constant or a variable for each variable of the pattern. We give two kinds of algorithms for both problems, a convolution-based method and an extended KMP-based method, and analyze their complexity.

Duel and Sweep Algorithm for Order-Preserving Pattern Matching

Given a text and a pattern over an alphabet, the classic exact matching problem searches for all occurrences of the pattern in the text. Unlike exact matching, order-preserving pattern matching (OPPM) considers the relative order of elements, rather t han their real values. In this paper, we propose an efficient algorithm for the OPPM problem using the “duel-and-sweep” paradigm. For a pattern of length m and a text of length n, our algorithm runs in \(O(n + m\log m)\) time in general, and in \(O(n + m)\) time under an assumption that the characters in a string can be sorted in linear time with respect to the string size. We also perform experiments and show that our algorithm is faster than the KMP-based algorithm.

Visualization and Analysis of Electrical Energy Consumption in Laboratories

Analyzing the electrical energy usage pattern of an institute is important in order to find a method to save electricity, because the usage of electrical energy is different depending on the laboratories in the building. In this paper, we report a system that we are developing to analyze and visualize the electric energy consumption of all laboratories in the building.

Drawing strategies for generalized tic-tac-toe (p, q)

GTTT(p, q) is an achievement game for polyominoes, which is an extension of Harary’s generalized tic-tac-toe. Two players alternately put p stones over a board with the exception that the first player Black puts q stones for the first move. The player who first achieves a given polyomino wins the game. Unlike the generalized tic-tac-toe, we define winner for polyomino that Black can achieve, loser that White can achieve, and draw that both players cannot achieve in each GTTT(p, q). In this paper we define three classes of polyominoes for GTTT(p, q) and show that any polyomino that satisfies some conditions for each classes is a draw.