Showing papers by "Andrzej Pelc published in 1996"

Fault‐tolerant broadcasting and gossiping in communication networks

Abstract: Broadcasting and gossiping are fundamental tasks in network communication. In broadcasting, or one-to-all communication, information originally held in one node of the network (called the source) must be transmitted to all other nodes. In gossiping, or all-to-all communication, every node holds a message which has to be transmitted to all other nodes. As communication networks grow in size, they become increasingly vulnerable to component failures. Thus, capabilities for fault-tolerant broadcasting and gossiping gain importance. The present paper is a survey of the fast-growing area of research investigating these capabilities. We focus on two most important efficiency measures of broadcasting and gossiping algorithms: running time and number of elementary transmissions required by the communication process. We emphasize the unifying thread in most results from the research in fault-tolerant communication: the trade-offs between efficiency of communication schemes and their fault-tolerance. © 1996 John Wiley & Sons, Inc.

Adaptive broadcasting with faulty nodes

Abstract: 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 cannot send information. Broadcasting is adaptive, i.e., a node schedules its next communication on the basis of information currently available to it. Assuming that the fraction of faulty nodes is bounded by a constant smaller than 1, we construct a broadcasting algorithm working in worst-case time O(log2 n).

Efficient gossiping by packets in networks with random faults

Abstract: Every node of a communication network has a constant size value which should be made known to all other nodes. Nodes and links fail independently with constant probabilities $p 0$ we present an algorithm to exchange values between all fault-free nodes of an n-node network in time $O(\frac{n}{b(n)}) + \log n$), with probability exceeding $1 - n^{ - \eta } $, for sufficiently large n. This order of magnitude of running time is optimal.

Broadcasting in synchronous networks with dynamic faults

Abstract: The problem of broadcasting in a network is to disseminate information from one node to all other nodes by transmitting it over communication links that connect nodes. We consider the time of broadcasting in the presence of at most k dynamic link failures. If a node knows source information, then in the next step all its neighbors connected by operational links also get to know it. Faults are dynamic, in the sense that a link may alternate arbitrarily between being operational or faulty, provided that, at every time step, the number of faulty links does not exceed k. The time bounds on broadcasting are considered with respect to two parameters: the number k of faulty links and the diameter d of the underlying graph. Broadcasting is guaranteed to be successful if and only if the edge connectivity of the network exceeds k, and we consider only such networks. For a fixed k, it is shown that broadcasting is always completed in time O(dk+1), where the bound is a function of diameter d. For a fixed d, it is shown that broadcasting is always completed in time O(kd/2–1), where the bound is a function of k. We prove that these orders of magnitude cannot be improved in general. Among networks, particularly interesting are those in which broadcasting time is close to their diameter in the presence of at most k dynamic faults, where k + 1 is the edge-connectivity of the network. We show that multidimensional tori have this property. © 1996 John Wiley & Sons, Inc.

Broadcasting with universal lists

Abstract: In broadcasting, information originally held in one node of a communication network (called the source) has to be transmitted to all other nodes. In a unit of time, every node which already received the source message can transmit it to one neighbor. In classical broadcasting, the choice of neighbors to be informed by a node and the order in which they are informed may depend on the source. Thus, nodes need to store many transmission lists corresponding to different possible sources and need to know the source to adapt their behavior accordingly. In this paper, we consider a variant of broadcasting in which every node is given a priori a single ordered list containing some of its neighbors. This list is meant to be universal for all possible sources. Upon obtaining the source message, a node transmits it to the neighbors from its list in prescribed order and then stops. This requires substantially less local memory devoted to schedule communication but usually increases broadcasting time. We compare broadcasting time in this and in the classical model and design optimal broadcasting schemes in the universal-list model for trees, rings, and grids. For tori and for complete graphs, we give upper bounds on broadcasting time.

Reliable Broadcasting in Hypercubes with Random Link and Node Failures

Abstract: We consider the problem of broadcasting in an n–node hypercube whose links and nodes fail independently with given probabilities p < 1 and q < 1, respectively. Information held in a fault-free node, called the source, has to reach all other fault-free nodes. Messages may be directly transmitted to adjacent nodes only, and every node may communicate with at most one neighbour in a unit of time. A message can be transmitted only if both communicating neighbours and the link joining them are fault-free. For parameters p and q satisfying (1 – p)(1 – q) ≽ 0.99 (e.g. p = q = 0.5%), we give an algorithm working in time O(log n) and broadcasting source information to all fault-free nodes with probability exceeding 1 – cn-e for some positive constant e, c depending on p and q but not depending on n.

Minimizing Congestion of Layouts for ATM Networks with Faulty Links

Abstract: We consider the problem of constructing virtual path layouts for an ATM network consisting of a complete network Kn of n processors in which a certain number of links may fail. Our main goal is to construct layouts which tolerate any configuration of up to f faults and have the least possible congestion. First, we study the minimal congestion of 1-hop f-tolerant layouts in Kn. For any positive integer f we give upper and lower bounds on this minimal congestion and construct f-tolerant layouts with congestion corresponding to the upper bounds. Our results are based on a precise analysis of the diameter of the network Kn[ℱ] which results from Kn by deleting links from a set ℱ of bounded size. Next we study the minimal congestion of h-hop f-tolerant layouts in Kn, for larger values of the number h of hops. We give upper and lower bounds on the order of magnitude of this congestion, based on results for 1-hop layouts. Finally, we consider a random, rather than worst case, fault distribution where links fail independently with constant probability p<1. Our goal now is to construct layouts with low congestion that tolerate the existing faults with high probability. For any p<1, we show the existence of 1-hop layouts in Kn, with congestion O(log n).

Minimizing Congestion of Layouts for ATM Networks with Faulty Links

Abstract: We consider the problem of constructing virtual path layouts for an ATM network consisting of a complete network K n of n processors in which a certain number of links may fail. Our main goal is to construct layouts which tolerate any configuration of up to f layouts and have a least possible congestion. First, we study the minimal congestion of 1-hop f-tolerant layouts in K n . For any positive integer f we give upper and lower bounds on this minimal congestion and construct f-tolerant layouts with congestion corresponding to the upper bounds. Our results are based on a precise analysis of the diameter of the network Kn[\(\mathcal{F}\)] which results from K n by deleting links from a set \(\mathcal{F}\) of bounded size. Next we study the minimal congestion of h-hop f-tolerant layouts in K n , for larger values of the number h of hops. We give upper and lower bounds on the order of magnitude of this congestion, based on results for 1-hop layouts. Finally, we consider a random, rather than worst case, fault distribution. Links fail independently with constant probability p}<1. Our goal now is to construct layouts with low congestion that tolerate the existing faults with high probability. For any p}<1, we show such layouts in K n , with congestion O(log n).

Fault-tolerant linear broadcasting

Abstract: In linear broadcasting, packets originally stored in one node, called the source, have to visit all other nodes of the network. Every packet has a predetermined route indicating in which order it visits the nodes. A faulty link or node of the network destroys all packets passing through it. A linear broadcasting scheme consisting of packets' routes is f-fault-tolerant if every fault-free node is visited by at least one packet for any configuration of at most f link or node failures. We estimate the minimum number of packets for which there exists an f-fault-tolerant linear broadcasting scheme in complete networks, and we construct schemes using few packets. Variations of this problem when faults can occur only in links or only in nodes are also considered.

The complexity of data mining on the Web

Abstract: We are witnessing the growth of the World Wide Web at an unprecedented speed. This expansion coincides with the growing use of the Internet for commercial purposes. It thus becomes plausible that users will be required to pay for navigating on the Web in the future. This is already the case to a certain extent, M some sites charge for access to particular Web pages (e.g., for on-line magazines or encyclopedias). It is even possible that access to particularly useful cat alogues of W WW pages will require payment. Moreover, telecommunication companies may start charging Internet access per use rather than a flat access fee. This situation makes it important to employ good strategies for searching the Web with a restricted budget. This paper proposes a model for thw task, under various assumptions regarding accem costs on the Web. We then investigate the complexity of finding optimal search strategies with a given budget and develop such strategies in several cases. The task of data mining on the Web is modeled as follows. Consider an undirected graph whose nodes are Web pages. Two nodes are adjacent if there is a hypertext link between them in at le@ one direction. Consider a user at a given home page ho. The user searches for data on a particular subject. From the point of view of this task, every Web page can be assigned an integer (positive or negative) value representing how closely its content matches the data sought by the user. The home page of the user has value O. It is reasonable to assume that values of adjacent nodes do not differ much. Indeed, pages represent ed by those nodes are joined by a hypertext link in at least one direction. Such pages are unlikely to have large difference in values from the point of view of a given data mining task. Suppose, for example, that the user seeks data on fault-tolerant routing in graphs and assigns the value v to the Web page algorithms on graphs. This page can have a hypertext link to faulttolerant algorithms on graphs, that will be of slightly larger value for our user, or a link to planarity testing, that slightly deviates from the subject, but is unlikely to have a hypertext link to Babylonian mythology, that would be clearly of much smaller value than v. We capture this phenomenon by assuming that if z and y are adjacent nodes then the difference of their values is either O or +1.

Approximate Maxima Finding of Continuous Functions Under Restricted Budget (Extended Abstract)

Abstract: A function is distributed among nodes of a graph in a“continuous” way, i.e., such that the difference between values stored at adjacent nodes is small. The goal is to find a node of maximum value by probing some nodes under a restricted budget. Every node has an associated cost which has to be paid for probing it and a probe reveals the value of the node. If the total budget is too small to allow probing every node, it is impossible to find the maximum value in the worst case. Hence we seek an Approximate Maxima Finding (AMF) algorithm that offers the best worst-case guarantee g, i.e., for any continuous distribution of values it finds a node whose value differs from the maximum value by at most g.