) Ajay K. Gupta ? Andreas G. Photiou Western Michigan University Lake States Insurance Company Kalamazoo, MI 49008, USA Traverse City, MI 49685, USA Abstract. We consider efficient algorithms for priority queues on distributed memory multiprocessors, such as nCUBE, iPSc, MPP and looselycoupled systems consisting of networked workstations. For a p-processor distributed memory multicomputer P and n data items in the priority queue, n ? p, we investigate two priority queues; horizontally sliced and vertically sliced. Both of these achieve load balance, i.e. at most \Theta(n=p) data items are stored at every processor of P . Horizontally sliced priority queue allows deletions and insertions of \Theta(p) items in time O( p bw øc + øpp log n) on hypercubic networks where øc is the communication time between a pair of processors, øp is the unit processing time and bw is the width of the communication channel between a pair of processors. Vertically sliced priority queue allows deletio...

In this paper we present an extensive study of many-to-many routing on trees under the matching routing model. Our study includes on-line and off-line algorithms. We present an asymptotically optimal on-line algorithm which routes k packets to their destination within d(k \Gamma 1) + d \Delta dist routing steps, where d is the degree of tree T on which the routing takes place and dist is the maximum distance any packet has to travel. We also present an off-line algorithm that solves the same problem within 2(k \Gamma 1)+dist steps. The analysis of our algorithms is based on the establishment of a close relationship between the matching and the hot-potato routing models that allows us to apply tools which were previously used exclusively in the analysis of hot-potato routing.

this paper we study the performance of the very first tournament based complete binary tree. We focus on discrete-event simulation and our results show that this unknown predecessor of heaps can be a more efficient alternative to the fastest pending event set implementations reported in the literature. We also extend the idea of binary tournaments to a (2; L)-tournament structure which exhibits the property of delaying the processing of events with larger timestamps whilst it keeps similar theoretical performance bounds to the native (2; 1)-structure or CBT. This property can be certainly useful in systems where many pending events are expected to be deleted or rescheduled during the simulation. 2 Tournament trees

We use an old idea of tournament based complete binary tree (CBT) to implement parallel priority queues (PQs). We show that this data structure enables a more efficient implementation of the operations extract-min and insert in terms of communications and synchronizations among processors than similar operations on the implicit heap. In most cases we only improve the asymptotic bounds on constant factors. However, some operations can be twice faster using simpler parallel algorithms upon the CBT. 1 Data structure and basic operations Every item stored in the PQ consists of a priority value and an indentifier. We associate every leaf of the CBT with one item, and use the internal nodes to maintain a continuous binary tournament among the items. A match, at internal node n, consists of determining the item with greater priority (less numerical value) between the two children of n and writing the identifier of the winner in n. The tournament is made up of a set of matches played in ever...

The bulk-synchronous parallel (BSP) model of computing has been proposed to enable the development of portable software which achieves scalable performance across diverse parallel architectures. A number of applications of computing science have been demonstrated to be efficiently supported by the BSP model in practice.

. Using EREW-PRAM algorithms on a tournament based complete binary tree we implement the insert and extract-min operations with p = log N processors at costs O(1) and O(log log N) respectively. Previous solutions [4, 7] under the PRAM model and identical assumptions attain O(log log N) cost for both operations. We also improve on constant factors the asymptotic bound for extract-min since in it we reduce the use of communication demanding primitives. The tournament tree enables the design of parallel algorithms that are noticeably simple. 1 Tournament trees Our data structure is a complete binary tree (CBT). Every item stored in the tree consists of a priority value and an identifier. We associate every leaf of the CBT with one item, and use the internal nodes to maintain a continuous binary tournament among the items. A match, at internal node n, consists of determining the item with higher priority (lesser numerical value) between the two children of n and writing the identifier of ...

In this paper we examine the problem of heap construction on a rooted tree T from a packet routing perspective. Each node of T initially contains a packet which has a key-value associated with it. The aim of the heap construction algorithm is to route the packets along the edges of the tree so that, at the end of the routing, the tree is heap ordered with respect to the key values associated with the packets. We consider the case where the routing is performed according to the matching model and we present and analyse an off-line algorithm that heap orders the tree within 2h(T) routing steps, where h(T) is the height of tree T. The main contribution of the paper is the novel analysis of the algorithm based on potential functions. It is our belief that potential functions will be the main vehicle in analysing fast non-recursive routing algorithms.