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Efficient Algorithms for the Minimum Shortest Path Steiner Arborescence Problem with Applications to VLSI Physical Design
"... Given an undirected graph G =(V;E) with positive edge weights (lengths) w: E!<+, a set of terminals (sinks) N V, and a unique root node r 2 N, a shortestpath Steiner arborescence (simply called an arborescence in the following) is a Steiner tree rooted at r spanning all terminals in N such thate ..."
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Cited by 39 (10 self)
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Given an undirected graph G =(V;E) with positive edge weights (lengths) w: E!<+, a set of terminals (sinks) N V, and a unique root node r 2 N, a shortestpath Steiner arborescence (simply called an arborescence in the following) is a Steiner tree rooted at r spanning all terminals in N such thatevery sourcetosink path is a shortest path in G. Given a triple (G; N; r), the Minimum ShortestPath Steiner Arborescence (MSPSA) problem seeks an arborescence with minimum weight. The MSPSA problem has various applications in the areas of VLSI physical design, multicast network communication, and supercomputer message routing; various cases have been studied in the literature. In this paper, we propose several heuristics and exact algorithms for the MSPSA problem with applications to VLSI physical design. Experiments indicate that our
Efficient PathBased Multicast in WormholeRouted Mesh Networks
"... The capability of multidestination wormhole allows a message to be propagated along any valid path in a wormholerouted network conforming to the underlying base routing scheme. The multicast on the pathbased routing model is highly depending on the spatial locality of destinations participating in ..."
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Cited by 4 (0 self)
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The capability of multidestination wormhole allows a message to be propagated along any valid path in a wormholerouted network conforming to the underlying base routing scheme. The multicast on the pathbased routing model is highly depending on the spatial locality of destinations participating in multicasting. In this paper, we propose two proximity grouping schemes for efficient multicast in wormholerouted mesh networks with multidestination capability by exploiting the spatial locality of the destination set. The rst grouping scheme, graphbased proximity grouping, is proposed to group the destinations with locality together to construct several disjoint submeshes. This is achieved by modeling the proximity grouping problem to graph partitioning problem. The second one, patternbased proximity grouping, is proposed by the pattern classi cation schemes to achieve the goal of the proximity grouping. By simulation results, we show the routing performance gains over the traditional Hamiltonian path routing scheme.
Tripbased Multicasting in Wormholerouted Networks
 in Proceedings of the 7th International Parallel Processing Symposium, (Newport Beach, CA
, 1993
"... In this paper, we consider the singlesource and multisource multicasting problem in wormholerouted networks. We propose a general ripbascl mocll for any network that has at least 2 virtual channels per physical channel. The underlying concept is a node sequence called skirbascl rip, which al ..."
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Cited by 1 (0 self)
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In this paper, we consider the singlesource and multisource multicasting problem in wormholerouted networks. We propose a general ripbascl mocll for any network that has at least 2 virtual channels per physical channel. The underlying concept is a node sequence called skirbascl rip, which always exists in graphs of any topology. Using such a sequence, we order nodes and edges to eliminate the possible cyclic dependency and develop a multicasting scheme. This scheme is simple, adaptive, distributed and deadlockfree.
IMPROVED ALGORITHMS FOR CONSTRUCTING HYPERCUBE SPMULTICASTING TREES
"... Given a source node s and a set of destinations D in the ncube we study the problem of constructing nearoptimal spmulticast trees. In other words, construct a nearoptimal Steiner tree for {s} ∪ D in which all paths from s to the destination nodes are shortest paths in the ncube. We discuss kno ..."
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Given a source node s and a set of destinations D in the ncube we study the problem of constructing nearoptimal spmulticast trees. In other words, construct a nearoptimal Steiner tree for {s} ∪ D in which all paths from s to the destination nodes are shortest paths in the ncube. We discuss known algorithms (Greedy, NGrouping, and Clustering) for the spmulticast tree problem and identify problem instances for which they perform poorly. We introduce three new algorithms (MOverlap, BEstimate and BUp) that identify structural similarities between the message destinations and avoid the pitfalls of the previously known algorithms. We present an experimental evaluation of all the algorithms over a wide range of problem instances. Our experimentation shows that the new algorithm BUp outperforms all the other methods.
Broadcasting on Unidirectional Hypercubes and Its Applications
, 2003
"... this paper, we present three kinds of broadcasting tree for the even dimensional unidirectional hypercube (UHC) and its applications (ASCEND/DESCEND algorithms and bitonic sorting). For the ndimensional UHC, under the constant evaluation model, one of our allport broadcasting trees has height n + ..."
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this paper, we present three kinds of broadcasting tree for the even dimensional unidirectional hypercube (UHC) and its applications (ASCEND/DESCEND algorithms and bitonic sorting). For the ndimensional UHC, under the constant evaluation model, one of our allport broadcasting trees has height n + 1, which is optimal. Whereas the best one of our oneport broadcasting trees needs at most 1 + n steps ) 6 mod ( ) 6 mod ( ( 3 3 n n n +  steps exactly). We also propose an allport faulttolerant broadcasting tree (a family of arcdisjoint spanning trees) whose height is no more than . 1 2 + n At last, we show that the ASCEND/DESCEND algorithms and bitonic sorting can be implemented in the UHC with the same complexity as the hypercube under the half duplex mode. All of our algorithms can be easily applied to the odd dimensional UHC
A FaultTolerant Routing Algorithm for 3D Torus Interconnection Networks
, 2003
"... This paper describes a new faulttolerant routing algorithm for 3D tori using the concept of “probability vectors”. To compute these vectors, a node determines first its faulty set, which represents the set of all its neighbouring nodes that are faulty or unreachable due to faulty links. Each node ..."
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This paper describes a new faulttolerant routing algorithm for 3D tori using the concept of “probability vectors”. To compute these vectors, a node determines first its faulty set, which represents the set of all its neighbouring nodes that are faulty or unreachable due to faulty links. Each node then calculates a probability vector, where the l th element represents the probability that a destination node at distance l cannot be reached through a minimal path due to a faulty node or link. The probability vectors are used by all the nodes to achieve an efficient faulttolerant routing in the network. An extensive performance evaluation conducted in this study reveals that the proposed algorithm exhibits good faulttolerance properties in terms of the achieved percentage of reachability and routing distances.
Regular Language Constrained Sequence Alignment Revisited
, 2011
"... Imposing constraints in the form of a finite automaton or a regular expression is an effective way to incorporate additional a priori knowledge into sequence alignment procedures. With this motivation, the Regular Expression Constrained Sequence Alignment Problem was introduced, which proposed an O( ..."
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Imposing constraints in the form of a finite automaton or a regular expression is an effective way to incorporate additional a priori knowledge into sequence alignment procedures. With this motivation, the Regular Expression Constrained Sequence Alignment Problem was introduced, which proposed an O(n 2 t 4) time and O(n 2 t 2) space algorithm for solving it, where n is the length of the input strings and t is the number of states in the input nondeterministic automaton. A faster O(n 2 t 3) time algorithm for the same problem was subsequently proposed. In this article, we further speed up the algorithms for Regular Language Constrained Sequence Alignment by reducing their worst case time complexity bound to O(n 2 t 3 /log t). This is done by establishing an optimal bound on the size of StraightLine Programs solving the maxima computation subproblem of the basic dynamic programming algorithm. We also study another solution based on a Steiner Tree computation. While it does not improve the worst case, our simulations show that both approaches are efficient in practice, especially when the input automata are dense.