We study deterministic algorithms for gossiping problem in ad hoc radio networks. The efficiency of communication algorithms in radio networks is very often expressed in terms of: maximum eccentricity D, maximum in-de...
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We study deterministic algorithms for gossiping problem in ad hoc radio networks. The efficiency of communication algorithms in radio networks is very often expressed in terms of: maximum eccentricity D, maximum in-degree Delta, and size (number of nodes) n of underlying graph of connections. The maximum eccentricity D of a network is the maximum of the lengths of shortest directed paths from a node u to a node v, taken over all ordered pairs (u, v) of nodes in the network. The maximum in-degree Delta of a network is the maximum of in-degrees of its nodes. We propose a new method that leads to several improvements in deterministic gossiping. It combines communication techniques designed for both known as well as unknown ad hoc radio networks. First we show how to subsume the O(Dn)-time bound yield by the round-robin procedure proposing a new (O) over tilde(rootDn)-time gossiping algorithm.(1) Our algorithm is more efficient than the known (O) over tilde (n(3/2))-time gossiping algorithms [Proc. 41st IEEE Symp. on Found. of Computer Science, 2000, pp. 575-581;Proc. 13th ACM-SIAM Symp. on Discrete algorithms, 2002], whenever D = O(n(alpha)) and alpha < 1. For large values of maximum eccentricity D, we give another gossiping algorithm that works in time O(DDelta(3/2) log(3) n) which subsumes the O(DDelta(2) log(3) n) upper bound presented in [Proc. 20th ACM Symp. on Principles of Distributed Computing, 2001, pp. 255-263]. Finally, we observe that for any so-called oblivious (i.e., non-adaptive) deterministic gossiping algorithm, any natural n and 1 less than or equal to D less than or equal to n-1, there is an unknown ad hoc radio network of size n and maximum eccentricity D which requires Omega(Dn) time-steps to complete gossiping. (C) 2001 Elsevier Science B.V. All rights reserved.
We consider the polymatroid packing and covering problems. The polynomial tune algorithm with the best approximation bound known for either problem is the greedy algorithm, yielding guaranteed approximation factors of...
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We consider the polymatroid packing and covering problems. The polynomial tune algorithm with the best approximation bound known for either problem is the greedy algorithm, yielding guaranteed approximation factors of 1/k for polymatroid packing and H(k) for polymatroid covering;where k: is the largest rank of an element in a polymatroid;and H(k) = Sigma(i=1)(k) 1/i is the kth Harmonic number. The main contribution of this note is to improve these bounds by slightly extending the greedy heuristics. Specifically, it will be shown how to obtain approximation factors of 2/(k + 1) for packing and H(k) - 1/6 for covering, generalizing some existing results on k-set packing;matroid matching, and k-set cover problems.
We present a significant improvement for parallel integer sorting. On the EREW (exclusive read exclusive write) PRAM our algorithm sorts n integers in the range {0, 1,..., m 1} in time O(log n) with O(n(q) (log n) ove...
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ISBN:
(纸本)0898714346
We present a significant improvement for parallel integer sorting. On the EREW (exclusive read exclusive write) PRAM our algorithm sorts n integers in the range {0, 1,..., m 1} in time O(log n) with O(n(q) (log n) over bar /k) operations using word length k log( m + n), where 1 less than or equal to k less than or equal to log n. In this paper we present the following four variants of our algorithm. (1) The first variant sorts integers in {0, 1,..., m - 1} in time O(log n) and in linear space with O(n) operations using word length log m log n. (2) The second variant sorts integers in {0, 1,..., n - 1} in time O ( log n) and in linear space with O(n rootlog n) operations using word length log n. (3) The third variant sorts integers in {0, 1,..., m - 1} in time O(log(3)/(2)n) and in linear space with O(n rootlog n) operations using word length log(m + n). (4) The fourth variant sorts integers in {0, 1,..., m - 1} in time O(log n) and space O(nm(epsilon)) with O(n rootlog n) operations using word length log( m + n). Our algorithms can then be generalized to the situation where the word length is k log( m + n), 1 less than or equal to k less than or equal to log n.
The shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in ...
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The shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The Shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one node to another often gives the best way to route message between the nodes. This paper presents an O(n 2 ) time algorithm for solving all pairs shortest path problems on trapezoid graphs which are extensions of interval graphs and permutation graphs. The space complexity of this algorithm is of O(n 2 ). This problem has been solved by constructing n breadth-first search (BFS) trees with each of the n vertices as root. As the lower bound of time complexity for computing the all pairs shortest paths is known to be of O(n 2 ), this proposed algorithm is optimal.
For trees, we define the notion of the so-called symmetry number to measure the size of the maximum subtree that exhibits an axial symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a ...
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For trees, we define the notion of the so-called symmetry number to measure the size of the maximum subtree that exhibits an axial symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a polynomial time algorithm for computing the symmetry number. (C) 2001 Elsevier Science B.V. All rights reserved.
The maximum weight k-independent set problem has applications in many practical problems like k-machines job scheduling problem, k-colourable subgraph problem, VLSI design layout and routing problem. Based on DAG (Dir...
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The maximum weight k-independent set problem has applications in many practical problems like k-machines job scheduling problem, k-colourable subgraph problem, VLSI design layout and routing problem. Based on DAG (Directed Acyclic Graph) approach, an O (kn(2)) time sequential algorithm is designed in this paper to solve the maximum weight k-independent set problem on weighted trapezoid graphs. The weights considered here are all non-negative and associated with each of the n vertices of the graph.
We present a simple and efficient algorithm for the problem of optimal covering augmentation for graphic polymatroids. We make a simple modification to the greedy algorithm for polymatroids of Edmonds [Proc. Calgary I...
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We present a simple and efficient algorithm for the problem of optimal covering augmentation for graphic polymatroids. We make a simple modification to the greedy algorithm for polymatroids of Edmonds [Proc. Calgary Internat. Conf. on Combinatorial Structures, 1970, pp. 69-87] so that it terminates in fewer steps. Our algorithm is far simpler yet as efficient as the previous best algorithm of Gabow [J. algorithms 26 (1998) 48-86]. It may also be noted that our algorithm is indeed an efficient algorithm for the general problem of performing min-cost augmentation of a feasible vector to a base of a graphic polymatroid. (C) 2001 Published by Elsevier Science B.V.
This paper proposes a general approach to design the optimal 1-fair alternators. An alternator is a network of concurrent processors, which can stabilize to states satisfying two conditions. First, if one processor is...
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This paper proposes a general approach to design the optimal 1-fair alternators. An alternator is a network of concurrent processors, which can stabilize to states satisfying two conditions. First, if one processor is executing the critical step, then no neighbor of that processor executes the critical step at the same time. Second, along any concurrent execution, each processor executes the critical step infinitely often. An alternator is said to be 1-fair if the second condition is changed as: For any x, t1 and t2, processor x executes two successive critical steps at steps t1 and t2, then in the period of steps [tl, t2), all other processors execute the critical step exactly once. A 1-fair alternator design is optimal if each processor can execute the critical step once in every fewest possible steps. Adopting this approach, we have demonstrated two optimal 1-fair alternator designs: one for hypercubes and the other for D x D meshes with odd D. For both designs, each processor executes the critical step once in every two steps. (C) 2001 Elsevier Science B.V. All rights reserved.
We present a derivation of Dijkstra's shortest path algorithm [Numer. Math. 1 (1959) 83]. We view the problem as computation of a "greatest solution" of a set of equations. A UNITY-style computation [Cha...
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We present a derivation of Dijkstra's shortest path algorithm [Numer. Math. 1 (1959) 83]. We view the problem as computation of a "greatest solution" of a set of equations. A UNITY-style computation [Chandy and Misra, Parallel Program design: A Foundation, 1988] is then prescribed whose implementation results in Dijkstra's algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.
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