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98
Programming a Hypercube Multicomputer
, 1988
"... We describe those features of distributed memory MIMD hypercube multicomputers that are necessary to obtain efficient programs. Several examples are developed. These illustrate the effectiveness of different programming strategies. ..."
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Cited by 33 (4 self)
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We describe those features of distributed memory MIMD hypercube multicomputers that are necessary to obtain efficient programs. Several examples are developed. These illustrate the effectiveness of different programming strategies.
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 29 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation 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.
Interval Routing Schemes
, 1998
"... Interval routing was introduced to reduce the size of routing tables: a router finds the direction where to forward a message by determining which interval contains the destination address of the message, each interval being associated to one particular direction. This way of implementing a routin ..."
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Cited by 29 (6 self)
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Interval routing was introduced to reduce the size of routing tables: a router finds the direction where to forward a message by determining which interval contains the destination address of the message, each interval being associated to one particular direction. This way of implementing a routing function is quite attractive but very little is known about the topological properties that must satisfy a network to support an interval routing function with particular constraints (shortest paths, limited number of intervals associated to each direction, etc.). In this paper we investigate the study of the interval routing functions. In particular, we characterize the set of networks which support a linear or a linear strict interval routing function with only one interval per direction. We also derive practical tools to measure the efficiency of an interval routing function (number of intervals, length of the paths, etc.), and we describe large classes of networks which support optimal (linear) interval routing functions. Finally, we derive the main properties satisfied by the popular networks used to interconnect processors in a distributed memory parallel computer.
A Routing and Broadcasting Scheme on Faulty Star Graphs
 IEEE Transactions on Computers
, 1993
"... In this paper we present a routing algorithm that uses the depth first search approach combined with a backtracking technique to route messages on the star graph in the presence of faulty links. The algorithm is distributed and requires no global knowledge of faults. The only knowledge required at a ..."
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Cited by 20 (2 self)
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In this paper we present a routing algorithm that uses the depth first search approach combined with a backtracking technique to route messages on the star graph in the presence of faulty links. The algorithm is distributed and requires no global knowledge of faults. The only knowledge required at a node is the state of its incident links. The routed message carries information about the followed path and the visited nodes. The algorithm routes messages along the optimal, i.e., the shortest path if no faults are encountered or if the faults are such that an optimal path still exists. In the absence of an optimal path, the algorithm always finds a path between two nodes within a bounded number of hops if the two nodes are connected. Otherwise, it returns the message to the originating node. We provide a performance analysis for the case where an optimal path does not exist. We prove that for a maximum of n \Gamma 2 faults on a graph with N = n! nodes, at most 2i + 2 steps are added to t...
On the runtime and robustness of randomized broadcasting
 In Proc. of ISAAC’ 06
, 2006
"... Abstract. One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. I ..."
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Cited by 15 (5 self)
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Abstract. One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol. At some time t an information r is placed at one of the nodes of a graph. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. In this work, we develop tight bounds on the runtime of the algorithm described above, and analyze its robustness. First, it is shown that on Δregular graphs this algorithm requires at least log2 − 1 N +log Δ
A Structural Approach to Graph Compression
 In MFCS Workshop on Communications
, 1998
"... We consider graph compression in terms of graph families. In particular, we show that graphs of bounded genus can be compressed to O(n) bits, where n is the number of vertices. We identify a property based on separators that makes O(n)bit compression possible for some graphs of bounded arboricit ..."
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Cited by 14 (1 self)
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We consider graph compression in terms of graph families. In particular, we show that graphs of bounded genus can be compressed to O(n) bits, where n is the number of vertices. We identify a property based on separators that makes O(n)bit compression possible for some graphs of bounded arboricity. 1 Introduction Graph representation as a data compression problem Lossless data compression is a process of representing a body of data by another body of data of smaller size from which the original data can be completely reconstructed. In the past thirty years a great deal of work has been done on the theory and practice of text compression (e.g., printed text or program source code) and of digitized data (e.g., voice or images). In fact, data compression has become a wellestablished subject in computer science, information theory, and communication theory. In contrast, very little has been done on compressing graphs. Since graphs are encountered everywhere and are often of very la...
Broadcasting vs. mixing and information dissemination on Cayley graphs
 In 24th Int. Symp. on Theor. Aspects of Computer Science (STACS
, 2007
"... Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succe ..."
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Cited by 13 (6 self)
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Abstract. One frequently studied problem in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following randomized broadcasting protocol: At some time t an information r is placed at one of the nodes of a graph G. In the succeeding steps, each informed node chooses one neighbor, independently and uniformly at random, and informs this neighbor by sending a copy of r to it. First, we consider the relationship between randomized broadcasting and random walks on graphs. In particular, we prove that the runtime of the algorithm described above is upper bounded by the corresponding mixing time, up to a logarithmic factor. One key ingredient of our proofs is the analysis of a continuoustype version of the afore mentioned algorithm, which might be of independent interest. Then, we introduce a general class of Cayley graphs, including (among others) Star graphs, Transposition graphs, and Pancake graphs. We show that randomized broadcasting has optimal runtime on all graphs belonging to this class. Finally, we develop a new proof technique by combining martingale tail estimates with combinatorial methods. Using this approach, we show the optimality of our algorithm on another Cayley graph and obtain new knowledge about the runtime distribution on several Cayley graphs. 1
Optimal information dissemination in Star and Pancake networks
, 1996
"... This paper presents a new decomposition technique for hierarchical Cayley graphs. This technique yields a very easy implementation of the divide and conquer paradigm for some problems on very complex architectures as the star graph or the pancake. As applications, we introduce algorithms for broadca ..."
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Cited by 12 (0 self)
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This paper presents a new decomposition technique for hierarchical Cayley graphs. This technique yields a very easy implementation of the divide and conquer paradigm for some problems on very complex architectures as the star graph or the pancake. As applications, we introduce algorithms for broadcasting and prefixlike operations that improve the best known bounds for these problems. We also give the first nontrivial optimal gossiping algorithms for these networks. In stargraphs and pancakes with N = n! processors, our algorithms take less than dlog Ne+ 1:5n steps. 1 Introduction The success of a parallel computer topology depends heavily on two points: ffl the existence of efficient communication schemes, ffl the existence of programming paradigms that facilitate the design of algorithms. This fact can be witnessed by the large number of machines based on the hypercube interconnection network, for which optimal information dissemination algorithms exist, and divide and conquer ...
MacroStar Networks: Efficient LowDegree Alternatives to Star Graphs for LargeScale Parallel Architectures
 IEEE Trans. Parallel Distrib. Sys
, 1996
"... We propose a new class of interconnection networks called macrostar networks, which belong to the class of Cayley graphs and use the star graph as a basic building module. A macrostar network can have node degree that is considerably smaller than that of a star graph of the same size, and diameter ..."
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Cited by 11 (5 self)
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We propose a new class of interconnection networks called macrostar networks, which belong to the class of Cayley graphs and use the star graph as a basic building module. A macrostar network can have node degree that is considerably smaller than that of a star graph of the same size, and diameter that is asymptotically within a factor of 1.25 from a universal lower bound (given its node degree) . We show that algorithms developed for star graphs can be emulated on suitably constructed macrostars with asymptotically optimal slowdown. In particular, we obtain asymptotically optimal algorithms to execute the multinode broadcast and total exchange communication tasks in a macrostar network, under both the singleport and the allport communication models. 1 Introduction A large variety of topologies have been proposed and analyzed in the literature [1, 11, 12, 14, 15, 17, 18, 19, 20, 23, 26, 30, 31] for the interconnection of processors in parallel computer systems. Among them, the ...
Selection, Routing, and Sorting on the Star Graph
 Proceedings of the International Parallel Processing Symposium
, 1993
"... We consider the problems of selection, routing and sorting on an nstar graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to desi ..."
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Cited by 10 (3 self)
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We consider the problems of selection, routing and sorting on an nstar graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs a sequence of n prefix computations in O(n 2) time. This algorithm is used as a subroutine in our other algorithms. We also show that sorting can be performed on the nstar graph in time O(n 3) and that selection of a set of uniformly distributed n keys can be performed in O(n 2) time with high probability. Finally, we also present a deterministic (non oblivious) routing algorithm that realizes any permutation in O(n 3) steps on the nstar graph. There exists an algorithm in the literature that can perform a single prefix computation in O(n lg n) time. The best known previous algorithm for sorting has a run time of O(n 3 lg n) and is deterministic. To our knowledge, the problem of selection has not been considered before on the star graph. 1