Simulating the CRCW PRAM on reconfigurable networks

AbstractThis paper addresses the problem of simulating the CRCW PRAM on reconfigurable networks. Let N and M, respectively, be the numbers of processors and memory cells contained in the CRCW PRAM. We firstly show that a two-dimensional N × MN1r reconfigurable network can simulate any operation performed on the CRCW PRAM in O(1) time, where r ⩾ 2 and is a constant. Then, if N ⩽ M, we further show that any operation performed on the CRCW PRAM can be simulated as well as O(1) time on a r-dimensional N1(r − 1) × N1(r − 1) × … × N1(r − 1) × (MN(r − 2)(r − 1)) reconfigurable network, where r ⩾ 2 and is a constant

Finding the conditional location of a median path on a tree

[[abstract]]©2008 Elsevier-In this paper, we study the problem of locating a median path of limited length on a tree under the condition that some existing facilities are already located. The existing facilities may be located at any subset of vertices. Upper and lower bounds are proposed for both the discrete and continuous models. In the discrete model, a median path is not allowed to contain partial edges. In the continuous model, a median path may contain partial edges. The proposed upper bounds for these two models are O(n log n) and O(n log nα(n)), respectively. They improve the previous known bounds from O(n log2 n) and O(n2), respectively. The proposed lower bounds are both Ω(n log n).[[department]]資訊工程學

Constant time sorting on a processor array with a reconfigurable bus system

[[abstract]]The authors constant time sorting algorithm on a three-dimensional processor array equipped with a reconfigurable bus system, which is far more feasible than the CRCW PRAM model. The processor array consists of N triangular arrays who bottom processors are connected into an N×N square array, where N is the number of data items to be sorted. The sorting algorithm is based on the well-known enumeration sort (also known as sorting by ranking). Data input, data comparisons, and data output are performed on the square array. The triangular arrays are responsible for ranking the data items during the sorting process.[[fileno]]2030215010021[[department]]資訊工程學

Efficient algorithms for the ring loading problem with demand splitting

[[abstract]]Given a ring of size n and a set K of traffic demands, the ring loading problem with demand splitting (RLPW) is to determine a routing to minimize the maximum load on the edges. In the problem, a demand between two nodes can be split into two flows and then be routed along the ring in different directions. If the two flows obtained by splitting a demand are restricted to integers, this restricted version is called the ring loading problem with integer demand splitting (RLPWI). In this paper, efficient algorithms are proposed for the RLPW and the RLPWI. Both the proposed algorithms require O(|K|+t s ) time, where t s is the time for sorting |K| nodes. If for some small constant , integer sort can be applied and thus t s =O(|K|);otherwise, . The proposed algorithms improve the previous upper bounds from O(n|K|) for both problems.[[fileno]]2030215030014[[department]]資訊工程學

A Faster Algorithm for Computing the Kernel of Maximum Agreement Subtrees

International audienceThe maximum agreement subtree method determines the consensus of a collection of phylogenetic trees by identifying maximum cardinality subsets of leaves for which all input trees agree. The trees induced by these maximum cardinality subsets are maximum agreement subtrees (MASTs). A single MAST may be misleading, since there can exist two MASTs which share almost no leaves; nevertheless, it may be impossible to inspect all MASTs, since the number of MASTs can be exponential in the number of leaves. To overcome this drawback, Swenson et al. suggested to further summarize the information common to all MASTs by their intersection, which is called the kernel agreement subtree (KAST). The construction of the KAST is the focus of this paper. Swenson et al. had an O(kn3 + n4 + nd+1) time algorithm for computing the KAST of k trees on n leaves, in which at least one tree has maximum degree d. In this paper, an O(kn3 + nd)-time algorithm is presented. We demonstrate the efficiency of our algorithm on simulated trees as well as on ribosomal RNA alignments, where trees with 13,000 taxa took only hours to process, whereas the previous algorithm did not terminate after a week of computation

A Faster Algorithm for Computing the Kernel of Maximum Agreement Subtrees

International audienceThe maximum agreement subtree method determines the consensus of a collection of phylogenetic trees by identifying maximum cardinality subsets of leaves for which all input trees agree. The trees induced by these maximum cardinality subsets are maximum agreement subtrees (MASTs). A single MAST may be misleading, since there can exist two MASTs which share almost no leaves; nevertheless, it may be impossible to inspect all MASTs, since the number of MASTs can be exponential in the number of leaves. To overcome this drawback, Swenson et al. suggested to further summarize the information common to all MASTs by their intersection, which is called the kernel agreement subtree (KAST). The construction of the KAST is the focus of this paper. Swenson et al. had an O(kn3+n4+nd+1)timealgorithmforcomputingtheKASTofktreesonnleaves,inwhichatleastonetreehasmaximumdegreed.Inthispaper,anO(kn^3 + n^d)$ -time algorithm is presented. We demonstrate the efficiency of our algorithm on simulated trees as well as on ribosomal RNA alignments, where trees with 13,000 taxa took only hours to process, whereas the previous algorithm did not terminate after a week of computation