The Pattern Matching problem with Swaps consists in finding all occurrences of a pattern P in a text T, when disjoint local swaps in the pattern are allowed. In the Approximate Pattern Matching problem with Swaps one ...
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The Pattern Matching problem with Swaps consists in finding all occurrences of a pattern P in a text T, when disjoint local swaps in the pattern are allowed. In the Approximate Pattern Matching problem with Swaps one seeks, for every text location with a swapped match of P, the number of swaps necessary to obtain a match at the location. In this paper we devise two general algorithms for both Standard and Approximate Pattern Matching with Swaps, named CROSS-SAMPLING and BACKWARD-CROSS-SAMPLING, with a O(nm) and O(nm(2)) worst-case time complexity, respectively. Then we provide efficient implementations of them, based on bit-parallelism, which achieve O(n) and O(nm) worst-case time complexity, with patterns v-hose length is comparable to the word-size of the target machine. From an extensive comparison with. some of the most Live algorithms for the matching problem, it turns out that our algorithms a) very flexible and achieve very good results in practice.
The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs with n vertices and m edges takes O( K(G) mn(1.5)) time, where K(G) is th...
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The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs with n vertices and m edges takes O( K(G) mn(1.5)) time, where K(G) is the vertex connectivity of G. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takes O(n(2)) time and O(n) space for a trapezoid graph.
Based on the geometric representation, an efficient algorithm is designed to find all articulation points of a permutation graph. The proposed algorithm takes only O(n log n) time and O(n) space, where n represents th...
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Based on the geometric representation, an efficient algorithm is designed to find all articulation points of a permutation graph. The proposed algorithm takes only O(n log n) time and O(n) space, where n represents the number of vertices. The proposed sequential algorithm can easily be implemented in parallel which takes O(log n) time and O(n) processors on an EREW PRAM. These are the first known algorithms for the problem on this class of graph.
In this paper, we study the net adding problem arising in VLSI layout process. Given a layout H and a new net N, we attempt to add net N to layout H without changing H. We present an efficient method to find a solutio...
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In this paper, we study the net adding problem arising in VLSI layout process. Given a layout H and a new net N, we attempt to add net N to layout H without changing H. We present an efficient method to find a solution or report there is no solution to the given problem. Our solution is optimal in minimizing the number of vias required in two-terminal cases, and nearly optimal in multi-terminal cases.
An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takes O(log n) time using O(n(2)/log n) processors on an EREW PRAM, provided the graph has at most O(n...
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An efficient parallel algorithm is presented to find a maximum weight independent set of a permutation graph which takes O(log n) time using O(n(2)/log n) processors on an EREW PRAM, provided the graph has at most O(n) maximal independent sets. The best known parallel algorithm takes O(log(2) n) time and O(n(3)/log n) processors on a CREW PRAM.
In this paper, an algorithm is designed to find a maximum weight independent set of a circular-arc graph with n vertices. The weights considered here are all non-negative real numbers and associated with each of the v...
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In this paper, an algorithm is designed to find a maximum weight independent set of a circular-arc graph with n vertices. The weights considered here are all non-negative real numbers and associated with each of the vertex of the graph. The proposed algorithm runs in time O(n(2)). Here we shown that the program slots of television channels during 24 hours can be modeled as a circular-arc graph. Each program represents a vertex and number of viewers of that program represents the weight of the corresponding vertex. Two vertices are connected by an edge iff the corresponding program slots have a common program time, i.e., if I-i and I-j are the program slots of two programs i and j then the corresponding vertices i and j are connected by an edge iff I-i boolean AND I-j not equal phi. We also shown that the non-overlapping program slots with maximum number of viewers can be selected by computing maximum weight independent set on the corresponding circular-arc graph.
Consider a simple undirected graph G = (V, E) with vertex set V and edge set E. Let G - u be a subgraph induced by the vertex set V - (u). The distance delta(G)(x, y) is defined as the length of the shortest path betw...
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Consider a simple undirected graph G = (V, E) with vertex set V and edge set E. Let G - u be a subgraph induced by the vertex set V - (u). The distance delta(G)(x, y) is defined as the length of the shortest path between vertices x and y in G. The vertex u E V is a hinge vertex if there exist two vertices x, y is an element of V - {u} such that delta(G-u)(x,y) > delta(G)(x, y). Let U be a set consisting of all hinge vertices of G. The neighborhood of u is the set of all vertices adjacent to u and is denoted by N(u). We define d(u) = max{delta(G-u)(x, y) vertical bar delta(G-u)(x, y) > delta G(x, y), x, y is an element of N(u)} for u is an element of U as detour degree of u. A maximum detour hinge vertex problem is to find a hinge vertex u with maximum d(u) in G. In this paper, we proposed an algorithm to find the maximum detour hinge vertex on an interval graph that runs in O(n(2)) time, where n is the number of vertices in the graph.
A popular way to describe and build the DAWG or Directed Acyclic Word Graph of a string is by transformation of the corresponding subword tree. This transformation, which is not difficult to reverse, is easy to grasp ...
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A popular way to describe and build the DAWG or Directed Acyclic Word Graph of a string is by transformation of the corresponding subword tree. This transformation, which is not difficult to reverse, is easy to grasp and almost trivial to implement except for the assumed implication of a standard tree isomorphism algorithm. Here we point out a simple property of subword trees that makes checking tree isomorphism in this context a straightforward process, thereby simplifying the transformation significantly. Subword trees and DAWGs arise rather ubiquitously in applications of string processing, where they often play complementary roles. Efficient conversions are thus especially desirable. (C) 2001 Elsevier Science B.V. All rights reserved.
In this paper, we consider a variant of the well-known Steiner tree problem. Given a complete graph G = (V, E) with a cost function c : E -> R+ and two subsets R and R' satisfying R' subset of R subset of V...
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In this paper, we consider a variant of the well-known Steiner tree problem. Given a complete graph G = (V, E) with a cost function c : E -> R+ and two subsets R and R' satisfying R' subset of R subset of V, a selected-internal Steiner tree is a Steiner tree which contains (or spans) all the vertices in R such that each vertex in R' cannot be a leaf. The selected-internal Steiner tree problem is to find a selected-internal Steiner tree with the minimum cost. In this paper, we present a 2 rho-approximation algorithm for the problem, where p is the best-known approximation ratio for the Steiner tree problem. (c) 2007 Elsevier B.V. All rights reserved.
Let T = (V, E) be a tree with n nodes such that each node v is associated with a value-weight pair (val(v), w(v)), where the value val(v) is a real number and the weight w(v) is a positive integer. The density of a pa...
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Let T = (V, E) be a tree with n nodes such that each node v is associated with a value-weight pair (val(v), w(v)), where the value val(v) is a real number and the weight w(v) is a positive integer. The density of a path P = (v(1), v(2).....v(k)) is defined as Sigma(k)(i=1) val(i)/Sigma(k)(i=1)w(i). The weight of P, denoted by w(P), is Sigma(k)(i=1)w(i). Given a tree of n nodes, two integers w(min) and w(max), and a length lower bound L, we present a pseudo-polynomial O(w(max)nL)-time algorithm to find a maximum-density path P in T such that W-min <= w(P) <= w(max) and the length of P is at least L. (c) 2007 Elsevier B.V. All rights reserved.
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