For two integers k, l > 0 and an undirected multigraph G = (V, E), we consider the problem of augmenting G by the smallest number of new edges to obtain an l-edge-connected and k-vertex-connected multigraph. In thi...
详细信息
For two integers k, l > 0 and an undirected multigraph G = (V, E), we consider the problem of augmenting G by the smallest number of new edges to obtain an l-edge-connected and k-vertex-connected multigraph. In this paper we show that a (k - 1)-vertex-connected multigraph G can be made l-edge-connected and k-vertex-connected by adding at most max{l + 1, 2k - 4} surplus edges over the optimum in O( min{k,root n}kn(3) + n(4)) time, where n = vertical bar V vertical bar.
We consider the problem of distributed gossiping in radio networks of unknown topology. For radio networks of size n and diameter D, we present an adaptive deterministic gossiping algorithm of time O(NrootDn + n log(2...
详细信息
We consider the problem of distributed gossiping in radio networks of unknown topology. For radio networks of size n and diameter D, we present an adaptive deterministic gossiping algorithm of time O(NrootDn + n log(2) n) or O(n(1.5)). This algorithm is a tuned version of the fastest previously known gossiping algorithm due to Gasieniec and Lingas [1], and improves the time complexity by a poly-logarithmic factor.
A deterministic polynomial time algorithm is presented for finding the distinct-degree factorization of multivariate polynomials over finite fields. As a consequence, one can count the number of irreducible factors of...
详细信息
A deterministic polynomial time algorithm is presented for finding the distinct-degree factorization of multivariate polynomials over finite fields. As a consequence, one can count the number of irreducible factors of polynomials over finite fields in deterministic polynomial time, thus resolving a theoretical open problem of Kaltofen from 1987. (C) 2004 Elsevier Ltd. All rights reserved.
This paper presents algorithms for computing a minimum 3-way cut and a minimum 4-way cut of an undirected weighted graph G. Let G = (V, E) bean undirected graph with n vertices, m edges, and positive edge weights. Gol...
详细信息
This paper presents algorithms for computing a minimum 3-way cut and a minimum 4-way cut of an undirected weighted graph G. Let G = (V, E) bean undirected graph with n vertices, m edges, and positive edge weights. Goldschmidt and Hochbaum presented an algorithm for the minimum k-way cut problem with fixed k, that requires O (n(4)) and O (n(6)) maximum flow computations, respectively, to compute a minimum 3-way cut and a minimum 4-way cut of G. In this paper we first show some properties on minimum 3-way cuts and minimum 4-way cuts, which indicate a recursive structure of the minimum k-way cut problem when k = 3 and 4. Then, based on those properties, we give divide-and-conquer algorithms for computing a minimum 3-way cut and a minimum 4-way cut of G, which require O(n(3)) and O(n(4)) maximum flow computations, respectively.
This paper proposes a deterministic algorithm for block placement problem, based on Sequence-Pair (SP), unlike most of the previous approaches use simulated annealing (SA). An initial placement is obtained by a simple...
详细信息
ISBN:
(纸本)0780362535
This paper proposes a deterministic algorithm for block placement problem, based on Sequence-Pair (SP), unlike most of the previous approaches use simulated annealing (SA). An initial placement is obtained by a simple analytical method and an SP is extracted from the placement. Then the algorithm moves modules conceptually in +45 degree direction, and in -45 degree direction, alternately until the evaluation converges, utilizing the SP. Our experiments show the algorithm runs 100 times faster than SA, while keeping the same level of area and total wire length performance.
This paper proposes a deterministic algorithm for block placement problem,based on Sequence-Pair(SP),unlike most of the previous approaches use simulated annealing (SA).An initial placement is obtained by a simple ana...
详细信息
This paper proposes a deterministic algorithm for block placement problem,based on Sequence-Pair(SP),unlike most of the previous approaches use simulated annealing (SA).An initial placement is obtained by a simple analytical method and an SP is extracted from the *** the algorithm moves modules conceptually in +45 degree direction,and in -45 degree direction,alternately until the evaluation converges, utilizing the *** experiments show the algorithm runs 100 times faster than SA,while keeping the same level of area and total wire length performance.
We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261-267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the exis...
详细信息
We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261-267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields. In particular, we prove the existence of a deterministic algorithm which completely factors all monic polynomials of degree n over F-q, q odd, except possibly O(n(2) log(2) q/q) polynomials, using O(n(2+epsilon) log(2)q) arithmetical operations in F-q. (C) 2000 Elsevier Science B.V. All rights reserved.
Let G = (V, E) be a multigraph which has a designated vertex s is an element of V with an even degree. For two edges e(1) = (s, u(1)) and e(2) = (s, u(2)), we say that a multigraph G' is obtained from G by splitti...
详细信息
Let G = (V, E) be a multigraph which has a designated vertex s is an element of V with an even degree. For two edges e(1) = (s, u(1)) and e(2) = (s, u(2)), we say that a multigraph G' is obtained from G by splitting e(1) and e(2) at s if two edges e(1) and e(2) are replaced with a single edge (u(1), u(2)). It is known that all edges incident to s can be split without losing the edge-connectivity of G in V - s. This complete splitting plays an important role in solving many graph connectivity problems. The currently fastest algorithm for a complete splitting [14] runs in O(n(m + n log n) log n) time, where n = \V\ and m is the number of pairs of vertices between which G has an edge. Their algorithm is first designed for Eulerian multigraphs, and then extended for general multigraphs. Although the part for Eulerian multigraphs is simple, the rest for general multigraphs is considerably complicated. This paper proposes a much simpler O (n (m + n log n) log n) time algorithm for finding a complete splitting. A new edge-splitting theorem derived from our algorithm is also presented.
暂无评论