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Showing papers on "Communication complexity published in 1987"


Journal ArticleDOI
TL;DR: A new distributed algorithm is presented for constructing breadth first search (BFS) trees, a tree of shortest paths from a given root node to all other nodes of a network under the assumption of unit edge weights.
Abstract: A new distributed algorithm is presented for constructing breadth first search (BFS) trees. A BFS tree is a tree of shortest paths from a given root node to all other nodes of a network under the assumption of unit edge weights; such trees provide useful building blocks for a number of routing and control functions in communication networks. The order of communication complexity for the new algorithm is O(V^{1.6} + E) where V is the number of nodes and E the number of edges. For dense networks with E \geq V^{1.6} this order of complexity is optimum.

126 citations


Journal ArticleDOI
TL;DR: An algorithm is presented which efficiently generates “high quality” random sequences (quasirandom bit-sequences) from two independent semi-random sources.
Abstract: The semi-random source, defined by Santha and Vazirani, is a general mathematical mode for imperfect and correlated sources of randomness (physical sources such as noise dicdes). In this paper an algorithm is presented which efficiently generates “high quality” random sequences (quasirandom bit-sequences) from two independent semi-random sources. The general problem of extracting “high quality” bits is shown to be related to communication complexity theory, leading to a definition of strong communication complexity of a boolean function. A hierarchy theorem for strong communication complexity classes is proved; this allows the previous algorithm to be generalized to one that can generate quasi-random sequences from two communicating semi-random sources

117 citations


Journal ArticleDOI
TL;DR: A situation where each one of two processors has access to a different convex function fi, i = 1, 2, defined on a common bounded domain is considered, to determine protocols under which the number of exchanged messages is minimized.

68 citations



Journal ArticleDOI
TL;DR: In this paper, a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks is derived by simulating the general network by a linear array and then using a lower bound on the complexity of the problem on the linear array.
Abstract: The main result of this paper is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array Applications of this technique yield optimal bounds on the communication complexity of merging, ranking, uniqueness, and triangle-detection problems on a ring of processors Nontrivial near-optimal lower bounds on the communication complexity of distinctness, merging, and ranking on meshes and complete binary trees are also derived

60 citations


Book ChapterDOI
16 Aug 1987
TL;DR: A N- party identification and signature systems, based on Fiat and Shamir's single party systems, and another N-party signature system based on discrete-log problem, which have communication complexity 2N times that of the basic Fiat-Shamir systems.
Abstract: A number of alternative encryption techniques have been suggested for secure audio teleconferencing implementable on public switched network, in which the centralized facility, called bridge, does not hold any secret. The role of the bridge is to synchronously add simultaneous encrypted signals, modulo some known number, and then transmit the result to all the participants. Each terminal has a secret key, with which it can decrypt the above modular sum of encrypted signals to obtain the desired ordinary sum of cleartext signals. Secrecy of the systems is analyzed. Some of which are provably secure, assuming the existence of one way functions, and for the others we have partial cryptanalysis.We also present a N-party identification and signature systems, based on Fiat and Shamir's single party systems, and another N-party signature system based on discrete-log problem. Our systems have communication complexity 2N times that of the basic Fiat-Shamir systems (as compared to a factor of N2 in the direct application of the basic scheme to all pairs).

30 citations


Proceedings ArticleDOI
01 Jan 1987
TL;DR: Mehlhorn and Schmidt as mentioned in this paper showed that a function f with deterministic communication complexity n 2 can have Las Vegas communication complexity O(n), which is the best possible, because the deterministic complexity cannot be more than the square of the Las Vegas complexity for any function.
Abstract: Improving a result of Mehlhorn and Schmidt, a function f with deterministic communication complexity n2 is shown to have Las Vegas communication complexity O(n). This is the best possible, because the deterministic complexity cannot be more than the square of the Las Vegas communication complexity for any function.

27 citations


01 Jan 1987
TL;DR: This document considers task systems modeled by directed acyclic graphs in which nodes represent tasks and arcs express precedence constraints, and each task can be computed by a processor in one unit of time and considers the problem of finding schedules that minimize finishing time.
Abstract: : This document considers task systems modeled by directed acyclic graphs in which nodes represent tasks and arcs express precedence constraints, and each task can be computed by a processor in one unit of time. It is known that if there are only two processors or if the graph is a tree, then there are polynormal time algorithms for scheduling the graph in minimum time, but in general the minimum time scheduling problem is NP-complete. The communication cost of a schedule is the number of pairs (p ,x) such that processor p does not compute task x but computes an immediate successor of x ; that is, the result of x must be communicated to p. I consider the problem of finding schedules that minimize finishing time and among those, finding schedules that minimize communication. That the problem with two processors on an arbitrary graph is NP-complete. The problem with arbitrarily many processors on a tree is also NP-complete. The case of two processors on a tree is open in general, but tight bounds for two processors on the indirected complete ternary tree of height k : for minimum time, communication k-log3k + 3 is achievable, and communication k-log3k + 1 is necessary.

20 citations


Journal ArticleDOI
TL;DR: A new distributed breadth-first-search algorithm for graphs with worst-case communication and time complexities are both O(|V|2), where |V| is the number of vertices.

17 citations


Journal ArticleDOI
TL;DR: Given two processes, each having a total-ordered set ofn elements, this work presents a distributed algorithm for finding median of these 2n elements using no more than logn +O(√logn) messages, but if the elements are distinct, only logn -O(1) messages will be required.
Abstract: Given two processes, each having a total-ordered set ofn elements, we present a distributed algorithm for finding median of these 2n elements using no more than logn +O(źlogn) messages, but if the elements are distinct, only logn +O(1) messages will be required. The communication complexity of our algorithm is better than the previously known result which takes 2 logn messages.

13 citations


Journal ArticleDOI
TL;DR: This paper presents distributed algorithms for some graph problems on a network model of computation, including breadth-first and breadth-depth searches of graphs, recognition of directed acyclic graphs and strong connectedness, finding weights of all the shortest paths from a single source to all other nodes in a weighted directed acYclic graph, and analyzing activity networks.

Book ChapterDOI
02 Jan 1987
TL;DR: In this paper, the authors considered the problem of information sharing in a synchronous broadcasting network and gave an O(n log 2 p + p )-time algorithm, where p is the number of nodes in the broadcasting network.
Abstract: In this paper we consider a synchronous broadcasting network, a distributed computation model which represents communication networks that are used extensively in practice. We consider a basic problem of information sharing: the computation of the multiple identification function. That is, given a network of p processors, each of which contains an n -bit string of information, how can every processor compute efficiently the subset of processors which have the same information as itself? The problem was suggested by Yao as a generalization of the two-processor case studied in his classic paper on distributed computing (Yao, 1979). The naive way to solve this problem takes O( np ) communication time, where a time unit is the time to transfer one bit. We present an algorithm which takes advantage of properties of strings and is O ( n log 2 p + p ) time. A simulation of sorting networks by the distributed model yields an O ( n log p + p ) (impractical) algorithm. By applying Yao's probabilistic implementation of the two-processor case to both algorithm we get probabilistic versions (with small error) where n is replaced by log n in the complexity expressions. We also present lower bounds for the problem: an Ω( n ) and an Ω( p ) bound are shown.