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, an O(log n) time and O(nn'/log n) processors parallel algorithm is designed to generate all paths from leaf nodes to the root of a tree, where n' is the total number of such paths. Using this al...
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In this paper, an O(log n) time and O(nn'/log n) processors parallel algorithm is designed to generate all paths from leaf nodes to the root of a tree, where n' is the total number of such paths. Using this algorithm an O(log N) time and O((n(2)+N)/log n) processors parallel algorithm is designed to generate all maximal independent sets on permutation graphs, where n represents the number of vertices (nodes) N is the output size. Both the algorithms run on an EREW PRAM.
In this paper, we define the minimax flow problem and design an O(k . M(n, m)) time optimal algorithm for a special case of the problem in which the weights on arcs are either O or 1, where n is the number of vertices...
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In this paper, we define the minimax flow problem and design an O(k . M(n, m)) time optimal algorithm for a special case of the problem in which the weights on arcs are either O or 1, where n is the number of vertices, m is the number of arcs, k (where 1 less than or equal to k less than or equal to m) is the number of arcs with nonzero weights, and M(n;m) is the best time bound for finding a maximum flow in a network.
Effective and efficient scheduling in a dynamically changing environment is important for real-time control of manufacturing, computer, and telecommunication systems. This paper illustrates the algorithmic and analyti...
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Effective and efficient scheduling in a dynamically changing environment is important for real-time control of manufacturing, computer, and telecommunication systems. This paper illustrates the algorithmic and analytical issues associated with developing efficient and effective methods to update schedules on-line. We consider the problem of dynamically scheduling precedence-constrained jobs on a single processor to minimize the maximum completion time penalty. We first develop an efficient technique to reoptimize a rolling schedule when new jobs arrive. The effectiveness of reoptimizing the current schedule as a long-term on-line strategy is measured by bounding its performance relative to oracles that have perfect information about future job arrivals.
Given a textstring x of length n, the Minimal Augmented Suffix Tree (T) over cap (x) of x is a digital-search index that returns, for any query string w and in a number of comparisons bounded by the length of w, the m...
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Given a textstring x of length n, the Minimal Augmented Suffix Tree (T) over cap (x) of x is a digital-search index that returns, for any query string w and in a number of comparisons bounded by the length of w, the maximum number of nonoverlapping occurrences of w in x. It is shown that, denoting the length of x by n, (T) over cap (x) can be built in time O(n log(2) n) and space O(n log n), off-line on a RAM.
A sequence d of integers is a degree sequence if there exists a (simple) graph G such that the components of d are equal to the degrees of the vertices of G. The graph G is said to be a realization of d. We provide an...
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A sequence d of integers is a degree sequence if there exists a (simple) graph G such that the components of d are equal to the degrees of the vertices of G. The graph G is said to be a realization of d. We provide an efficient parallel algorithm to realize d;the algorithm runs in O(log n) time using O(n + m) CRCW PRAM processors, where n and m are the number of vertices and edges in G. Before our result, it was not known if the problem of realizing d is in NC.
We study two related problems motivated by molecular biology. Given a graph G and a constant k, does there exist a supergraph G' of G that is a unit interval graph and has clique size at most k? Given a graph G an...
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We study two related problems motivated by molecular biology. Given a graph G and a constant k, does there exist a supergraph G' of G that is a unit interval graph and has clique size at most k? Given a graph G and a proper k-coloring c of G, does there exist a supergraph G' of G that is properly colored by c and is a unit interval graph? We show that those problems are polynomial for fixed k. On the other hand, we prove that the first problem is equivalent to deciding if the bandwidth of G is at most k - 1. Hence, it is NP-hard and W[t]-hard for all t. We also show that the second problem is W[1]-hard. This implies that for fixed k, both of the problems are unlikely to have an O(n(alpha)) algorithm, where alpha is a constant independent of k. A central tool in our study is a new graph-theoretic parameter closely related to pathwidth. An unexpected useful consequence is the equivalence of this parameter to the bandwidth of the graph.
An extension of the disjoint set union problem is considered, where the extra primitive backtrack(i) can undo the last i unions not yet undone. Let n be the total number of elements in all the sets. A data structure i...
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An extension of the disjoint set union problem is considered, where the extra primitive backtrack(i) can undo the last i unions not yet undone. Let n be the total number of elements in all the sets. A data structure is presented that supports each union and find in O(log n/log log n) worst-case time and each backtrack(i) in O(1) worst-case time, irrespective of i. The total space required by the data structure is 0(n). A byproduct of this construction is a partially persistent data structure for the standard set union problem, capable of supporting union, find, and find-in-the-past operations, each in O(log n/log log n) worst-case time. All these upper bounds are tight for the class of separable-pointer algorithms as well as in the cell probe model of computation.
The algorithm presented in this paper generates each k-way forests of fixed size n, height h, and number of components c. Each random forest is generated in a linear number of operations in its size. The algorithm com...
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The algorithm presented in this paper generates each k-way forests of fixed size n, height h, and number of components c. Each random forest is generated in a linear number of operations in its size. The algorithm computes a table of values in a pre-processing phase. This table occupies O(hn2) locations and takes O(hn3) time to produce. This theory of information storage is proven in the different theorem presented in this paper.
We introduce the notion of k-violation linear programming. Given a set of n halplanes, we want to compute an optimal solution with respect to a given linear functional. However, in opposite to classical linear program...
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We introduce the notion of k-violation linear programming. Given a set of n halplanes, we want to compute an optimal solution with respect to a given linear functional. However, in opposite to classical linear programming [16], we allow to violate at most k of the n constraints, for some fixed k is an element of {0,...,n-1}. We solve this problem in O(beta(k)(n) time and O(n) space, where beta(k)(n) := n log + k log(2) k. This is optimal if k is an element of O(n(alpha)) for any fixed positive alpha < 1. The general idea behind our approach is a new approach is a new technique for computing a minimum of the k-level of an arrangement. Based on recent slope selecting techniques by Cole et al. [4] and Matousek [15], we develop an algorithm for computing a minimum k-level point in O(beta(k)(n)) time and linear space. Our result improves all existing approaches that explicitly compute the entire k-level [3,9,11]. The presented technique is of independent interest and can be applied to several other problems, as well.
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