Improved Algorithms for the Point-Set Embeddability problem for Plane 3-Trees

In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex is represented as a distinct point of $S$ as well as to provide an embedding if one does exist. Recently, in \cite{DBLP:conf/gd/NishatMR10}, a complete characterization for this problem on a special class of graphs known as the plane 3-trees was presented along with an efficient algorithm to solve the problem. In this paper, we use the same characterization to devise an improved algorithm for the same problem. Much of the efficiency we achieve comes from clever uses of the triangular range search technique. We also study a generalized version of the problem and present improved algorithms for this version of the problem as well

Sub-quadratic time and linear space data structures for permutation matching in binary strings

AbstractGiven a pattern P of length n and a text T of length m, the permutation matching problem asks whether any permutation of P occurs in T. Indexing a string for permutation matching seems to be quite hard in spite of the existence of a simple non-indexed solution. In this paper, we devise several o(n2) time data structures for a binary string capable of answering permutation queries in O(m) time. In particular, we first present two O(n2/logn) time data structures and then improve the data structure construction time to O(n2/log2n). The space complexity of the data structures remains linear

Computing a Longest Common Subsequence of two strings when one of them is Run Length Encoded

Abstract. Given two strings, the longest common subsequence (LCS) problem computes a common subsequence that has the maximum length. In this paper, we present new and efficient algorithms for solving the LCS problem for two strings one of which is run length encoded (RLE). We first present an algorithm that runs in O(gN) time, where g is the length of the RLE string and N is the length of uncompressed string. Then based on the ideas of the above algorithm we present another algorithm that runs in O(R log(log g) + N) time, where R is the total number of ordered pairs of positions at which the two strings match. Our first algorithm matches the best algorithm in the literature for the same problem. On the other hand, for R < gN / log(log)g, our second algorithm outperforms the best algorithms in the literature