A path cover of a graph G is a set of vertex-disjoint paths that cover all the vertices of G. An optimal path cover of G is a path cover of minimum cardinality. This problem is known to be NP-complete for arbitrary gr...
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A path cover of a graph G is a set of vertex-disjoint paths that cover all the vertices of G. An optimal path cover of G is a path cover of minimum cardinality. This problem is known to be NP-complete for arbitrary graphs. We present a linear algorithm for this problem on interval graphs. Given the adjacency lists of an interval graph with n vertices and m edges, our algorithm runs in O(m + n) time.
Using a linear time many-one reduction from the problem TOTAL DOMINATING SET to the problem DOMINATING SET we show how to obtain efficient algorithms to compute a minimum cardinality total dominating set on a variety ...
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Using a linear time many-one reduction from the problem TOTAL DOMINATING SET to the problem DOMINATING SET we show how to obtain efficient algorithms to compute a minimum cardinality total dominating set on a variety of graph classes, among them permutation graphs, dually chordal graphs and k-polygon graphs. (C) 1997 Elsevier Science B.V.
Rotation distances measure the difference in shape in rooted binary trees. We construct sharp bounds on maximal right-arm rotation distance and restricted right-arm rotation distance for trees of size n. These bounds ...
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Rotation distances measure the difference in shape in rooted binary trees. We construct sharp bounds on maximal right-arm rotation distance and restricted right-arm rotation distance for trees of size n. These bounds sharpen the results of Cleary and Taback and incorporate the lengths of the right side of the trees to improve the bounds. (c) 2007 Elsevier B.V. All rights reserved.
We consider a variant of the set union problem, called set union with arbitrary deunions, that consists of maintaining a collection of disjoint sets under three kinds of operations: union, find, and deunion (i). A deu...
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We consider a variant of the set union problem, called set union with arbitrary deunions, that consists of maintaining a collection of disjoint sets under three kinds of operations: union, find, and deunion (i). A deunion (i) undoes the ith union performed so far and not yet undone. Each operation can be supported in O(log n) time in the worst-case, where n is the total number of items in the collection of disjoint sets. Motivations for this problem arise in logic programming memory management.
The graph isomorphism problem has been much studied in the literature. Linear-time algorithms for the isomorphism problem have been obtained for trees, for planar graphs, for maximal outerplanar graphs, and for inter...
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The graph isomorphism problem has been much studied in the literature. Linear-time algorithms for the isomorphism problem have been obtained for trees, for planar graphs, for maximal outerplanar graphs, and for interval graphs. A linear-time algorithm is proposed for the isomorphism problem of a subclass of chordal graphs, namely, Hamiltonian 2-sep-chordal graphs. This class properly contains the class of mops. The polynomial transformation given by Leuker and Booth (1979) suffices to show that the isomorphism problem for 2-sep-chordal graphs is as hard as the general graph isomorphism problem. Consequently, it is of interest to study for what other subclasses of chordal graphs, in addition to trees, mops, and interval graphs, there exist polynomial time isomorphism solutions.
The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties of graphs with a given disk dimension ...
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The disk dimension of a planar graph G is the least number k for which G embeds in the plane minus k open disks, with every vertex on the boundary of some disk. Useful properties of graphs with a given disk dimension are derived, leading to an algorithm to obtain an outerplanar subgraph of a graph with disk dimension k by removing at most 2k - 2 vertices. This reduction is used to obtain linear-time exact and approximation algorithms on graphs with fixed disk dimension. In particular, a linear-time approximation algorithm is presented for the pathwidth problem. (c) 2006 Elsevier B.V. All rights reserved.
We present an algorithm to search for a pattern containing a sequence of don't care symbols in a preprocessed text. This problem models proximity searching in text searching systems and special searching problems ...
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We present an algorithm to search for a pattern containing a sequence of don't care symbols in a preprocessed text. This problem models proximity searching in text searching systems and special searching problems in biological sequences. The main result is that the suffix array data structure of Manber and Myers can be used to reduce this problem to the two-dimensional orthogonal range queries problem. Using known results for the latter problem we obtain a data structure that uses O(n(k + m)) space, where n is the size of the text, k is an upper bound on the number of don't care symbols and m is an upper bound on the number of characters of the pattern appearing before the don't care symbols. The number of occurrences of the pattern can be found in O(log n) time, and a list of all occurrences can be found in time O(n1/4 + R), where R is the number of occurrences.
This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number alpha such that Q[alpha] = F given a real Galois extension F of Q by its integ...
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This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number alpha such that Q[alpha] = F given a real Galois extension F of Q by its integral basis. This algorithm is based on the lattice reduction, and it runs in time polynomial in the size of the integral basis. Next, we show that for a fixed Pisot number alpha, one can compute [alpha(n)] (mod m) in time polynomial in (log(mn))(0(1)), where m and n are positive integers. (c) 2013 Elsevier B.V. All rights reserved.
A string w covers another string z if every position of z is within some occurrence of w in z. Clearly, every string is covered by itself. A string that is covered only by itself is superprimitive. We show that the pr...
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A string w covers another string z if every position of z is within some occurrence of w in z. Clearly, every string is covered by itself. A string that is covered only by itself is superprimitive. We show that the property of being superprimitive is testable on a string of n symbols in O(n) time and space.
The graph sandwich problem for property Phi is defined as follows: Given two graphs G(1) = (V, E-1) and G(2) = (V, E-2) such that E-1 subset of or equal to E-2, is there a graph G = (V, E) such that E-1 subset of or e...
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The graph sandwich problem for property Phi is defined as follows: Given two graphs G(1) = (V, E-1) and G(2) = (V, E-2) such that E-1 subset of or equal to E-2, is there a graph G = (V, E) such that E-1 subset of or equal to E subset of or equal to E-2 which satisfies property Phi? We present a polynomial-time algorithm for solving the graph sandwich problem, when property Phi is "to contain a homogeneous set". The algorithm presented also provides the graph G and a homogeneous set in G in case it exists. (C) 1998 Elsevier Science B.V. All rights reserved.
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