General Routing Algorithms for Star Graphs

In designing algorithms for a specific parallel architecture, a programmer has to cope with topological and cardinality variations. Both these problems always increase the programmer\u27s effort. However, an ideal shared memory abstract parallel model called the parallel random access machine (PRAM) [KRUS86, KRUS88] that avoids these problems and also simple-to-program has been proposed. Unfortunately, the PRAM does not seem to be realizable in the present or even foreseeable technologies. On the other hand, a packet routing technique can be employed to simulate the PRAM on a feasible parallel architecture without significant loss of efficiency. The problem of routing is also important due to its intrinsic significance in distributed processing and its important role in the simulations among parallel models. The routing problem is defined as follows: Given a specific network and a set of packets of information in which a packet is an (origin, destination) pair. To start with, the packets are placed on their origins, one per node. These packets must be routed in parallel to their own destinations such that at most one packet passes through any link of the network at any time and all packets arrive at their destinations as quickly as possible. We are interested in a special case of the general routing problem called permutation routing in which the destinations form some permutation of the origins. A routing algorithm is said to be oblivious if the path taken by each packet is only dependent on its source and destination. An oblivious routing strategy is preferable since it will lead to a simple control structure for the individual processing elements. Also oblivious routing algorithms can be used in a distributed environment. In this paper we are concerned with only oblivious routing strategies

A Unified approach to concurrent and parallel algorithms on balanced data structures

Concurrent and parallel algorithms are different. However, in the case of dictionaries, both kinds of algorithms share many common points. We present a unified approach emphasizing these points. It is based on a careful analysis of the sequential algorithm, extracting from it the more basic facts, encapsulated later on as local rules. We apply the method to the insertion algorithms in AVL trees. All the concurrent and parallel insertion algorithms have two main phases. A percolation phase, moving the keys to be inserted down, and a rebalancing phase. Finally, some other algorithms and balanced structures are discussed.Postprint (published version

Randomized Parallel Selection

We show that selection on an input of size N can be performed on a P-node hypercube (P = N/(log N)) in time O(n/P) with high probability, provided each node can process all the incident edges in one unit of time (this model is called the parallel model and has been assumed by previous researchers (e.g.,[17])). This result is important in view of a lower bound of Plaxton that implies selection takes Ω((N/P)loglog P+log P) time on a P-node hypercube if each node can process only one edge at a time (this model is referred to as the sequential model)

Sample sort on meshes

This paper provides an overview of lower and upper bounds for mesh-connected processor networks. Most attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Grammatikakis, Hsu and Kraetzl on multicomputer routing, submitted to JPDC

A Fast Scheduling Algorithm for WDM Optical Networks

Wavelength Division Multiplexing (WDM) is emerging as the most promising approach to exploit the huge bandwidth of optical fibre. This approach divides the optical spectrum into many different channels where each channel corresponds to a different wavelength. Single-hop WDM networks are attractive in local area environment where all the nodes can be connected to a single broadcast facility. In a single-hop WDM broadcast network, the transmitter must know when to transmit a packet and at which wavelength, while the receiver must know when to tune to the appropriate wavelength to receive the packet. This process requires some form of coordination. Many researches have focused on the scheduling algorithms that perform this kind of coordination. This thesis proposes a scheduling algorithm for the WDM broadcast networks. The algorithm employs a theory in graph, known as edge colouring of bipartite multigraph to produce the transmission schedule, which is free from collision due to the nature of the edge colouring. An optimal edge colouring of bipartite multi graph can be found in O(M log2 N) time, where M is number of packets selected for scheduling, and N is the number of the nodes. This time complexity can be improved to O(log3 N) by parallel processing using O(M) processors. Two variations of implementation of the scheduling algorithm have been proposed, namely the Variable Frame Size (VFS) and Limited Frame Size (LFS) schemes. These schemes use different criteria to select packets from the nodes for scheduling. The VFS scheme is simple, but supports only best effort transmissions. The LFS scheme ensures the frame size of the transmission schedule is bounded, thus enabling it to support bandwidth guarantee to the nodes up to a node's fair share of the network capacity. The LFS scheme is capable of supporting constant bit rate and unspecified bit rate service categories, analogous to the Asynchronous Transfer Mode (ATM) services. The results show that the LFS scheme performs better than the VFS scheme in terms of channel utilisation, packet loss probability and network throughput for all the simulated traffic patterns, especially at heavy loads. Besides, the LFS scheme respects any level of bandwidth guarantee, while the unused bandwidth can be used for best effort transmissions. The results also show that the VFS and LFS schemes are future-proof as they are able to capitalise on the increase in the number of wavelength channels

On Money as a Means of Coordination between Network Packets

In this work, we apply a common economic tool, namely money, to coordinate network packets. In particular, we present a network economy, called PacketEconomy, where each flow is modeled as a population of rational network packets, and these packets can self-regulate their access to network resources by mutually trading their positions in router queues. Every packet of the economy has its price, and this price determines if and when the packet will agree to buy or sell a better position. We consider a corresponding Markov model of trade and show that there are Nash equilibria (NE) where queue positions and money are exchanged directly between the network packets. This simple approach, interestingly, delivers improvements even when fiat money is used. We present theoretical arguments and experimental results to support our claims

Parallel and Distributed Computing

The 14 chapters presented in this book cover a wide variety of representative works ranging from hardware design to application development. Particularly, the topics that are addressed are programmable and reconfigurable devices and systems, dependability of GPUs (General Purpose Units), network topologies, cache coherence protocols, resource allocation, scheduling algorithms, peertopeer networks, largescale network simulation, and parallel routines and algorithms. In this way, the articles included in this book constitute an excellent reference for engineers and researchers who have particular interests in each of these topics in parallel and distributed computing