this article follows the aims stated above. The first section introduces this research area. The basic definitions are given and the fundamental, simple observations concerning the relations among the complexity measures defined are carefully explained. This section is

Abstract—We present efficient algorithms for two all-to-all communication operations in message-passing systems: index (or all-toall personalized communication) and concatenation (or all-to-all broadcast). We assume a model of a fully connected messagepassing system, in which the performance of any point-to-point communication is independent of the sender-receiver pair. We also assume that each processor has k ≥ 1 ports, through which it can send and receive k messages in every communication round. The complexity measures we use are independent of the particular system topology and are based on the communication start-up time, and on the communication bandwidth. In the index operation among n processors, initially, each processor has n blocks of data, and the goal is to exchange the i th block of processor j with the j th block of processor i. We present a class of index algorithms that is designed for all values of n and that features a trade-off between the communication start-up time and the data transfer time. This class of algorithms includes two special cases: an algorithm that is optimal with respect to the measure of the start-up time, and an algorithm that is optimal with respect to the measure of the data transfer time. We also present experimental results featuring the performance tuneability of our index algorithms on the IBM SP-1 parallel system. In the concatenation operation, among n processors, initially, each processor has one block of data, and the goal is to concatenate the n blocks of data from the n processors, and to make the concatenation result known to all the processors. We present a concatenation algorithm that is optimal, for most values of n, in the number of communication rounds and in the amount of data transferred. Index Terms—All-to-all broadcast, all-to-all personalized communication, complete exchange, concatenation operation, distributedmemory system, index operation, message-passing system, multiscatter/gather, parallel system.

This paper studies the problems of broadcasting and gossiping in optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. In this paper we consider both single--hop and multihop optical networks. In single--hop networks the information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high speed communication. In multi hop networks a packet may have to be routed through a few intermediate nodes before reaching its final destination. In both models, we give efficient broadcasting and gossiping algorithms, in terms of time and number of wavelengths. We consider both networks with arbitrary topologies and particular networks of practical interest. Several of our algorithms exhibit optimal performances. 1 Introduction Motivations. Op...

In this paper, we deal with the compact routing problem, that is implementing routing schemes that use a minimum memory size on each router. A universal routing scheme is a scheme that applies to all n-node networks. In [31], Peleg and Upfal showed that one can not implement a universal routing scheme with less than a total of \Omega\Gamma n 1+1=(2s+4) ) memory bits for any given stretch factor s 1. We improve this bound for stretch factors s, 1 s ! 2, by proving that any near-shortest path universal routing scheme uses a total of \Omega\Gamma n 2 ) memory bits in the worst-case. This result is obtained by counting the minimum number of routing functions necessary to route on all n-node networks. Moreover, and more fundamentally, we give a tight bound of \Theta(n log n) bits for the local minimum memory requirement of universal routing scheme of stretch factors s, 1 s ! 2. More precisely, for any fixed constant ", 0 ! " ! 1, there exists an n-node network G on which at least \O...

We survey routing problems on fixed-connection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, k-relation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.

In this paper, we deal with the compact routing problem, that is implementing routing schemes that use a minimum memory size on each router. In [20], Peleg and Upfal showed that there is no hope to do that with less than a total \Omega\Gamma n 1+1=(2s+4) ) memory bits for any stretch factor s 1. We improve this bound for stretch factors s ! 2 by proving that any near-shortest path routing scheme uses a total of \Omega\Gamma n 2 ) memory bits. 1 Introduction The general routing problem in a network (as opposed to the permutation routing problem [18] or the broadcasting problem [8]) consists of finding a routing protocol or routing function such that, for any source-destination pair, any message from the source can be routed to the destination. XY -routing [2] or e-cube routing [3] are such protocols. The efficiency of a protocol is measured in terms of latency (related to the length of the paths) and/or throughput (related to link or node congestion). Finding shortest paths in a n...

We consider broadcasting from a fault-free source to all nodes of a completely connected n-node network in the presence of k faulty nodes. Every node can communicate with at most one other node in a unit of time and during this period every pair of communicating nodes can exchange information packets. Faulty nodes can receive information but cannot send it. Broadcasting is adaptive, i.e. a node schedules its next communication on the basis of information currently available to it. We study worst case running time of fault-tolerant broadcasting algorithms in two models: in the wake-up model only nodes already having the source message can call other nodes and in the unrestricted model all fault-free nodes can call. In the first model we give an optimal algorithm working in time k +dlog(n \Gamma k)e. In the second model we give an algorithm working in time O(log 2 n), whenever the fraction of faulty nodes is bounded by a constant smaller than 1. Key words: adaptive, algorithm, broadc...

In a distributed system, each entity has a label (port number) associated to each of its neighbors. It is well known that if the labeling satisfies a global consistency property called Sense of Direction, the communication complexity of many distributed problem can be greatly reduced. This property is assumed to be present and it is implicitly used in most interconnection networks. In this paper we investigate the nature of the relationship between Sense of Direction and network topology. We first consider the class of labelings which only satisfy the requirement of local orientation; that is, at each node, the outgoing edges have distinct labels. We then consider the class of labelings which also satisfy edge symmetry; that is, there exists a correlation between the labels neighbors give to their connecting edge. This class includes most of used labelings. We completely characterize the interplay between topological constraints and consistency constraints for these two classes of labe...

Gossiping is an information dissemination problem in which each node of a communication network has a unique piece of information that must be transmitted to all other nodes using two-way communications between pairs of nodes along the communication links of the network. In this paper, we study gossiping using a linear cost model of communication which includes a start-up time and a propagation time which is proportional to the amount of information transmitted. A minimum linear gossip graph is a graph (modelling a network), with the minimum possible number of links, in which gossiping can be completed in minimum time under the linear cost model. For networks with an even number of nodes, we prove that the structure of minimum linear gossip graphs is independent of the relative values of the start-up and unit propagation times. We prove that this is not true when the number of nodes is odd. We present four infinite families of minimum linear gossip graphs. We also present minimum linea...

Abstract. The Wireless Gathering Problem is to find a schedule for data gathering in a wireless static network. The problem is to gather a set of messages from the nodes in the network at which they originate to a central node, representing a powerful base station. The objective is to minimize the time to gather all messages. The sending pattern or schedule should avoid interference of radio signals, which distinguishes the problem from wired networks. We study the Wireless Gathering Problem from a combinatorial optimization point of view in a centralized setting. This problem is known to be NP-hard when messages have no release time. We consider the more general case in which messages may be released over time. For this problem we present a polynomial-time on-line algorithm which gives a 4-approximation. We also show that within the class of shortest path following algorithms no algorithm can have approximation ratio better than 4. We also formulate some challenging open problems concerning complexity and approximability for variations of the problem. 1