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Sense of Direction: Definitions, Properties and Classes
"... An extensive body of evidence exists of the impact that specific edge labelings have on the communication complexity of distributed problems. It has been long suspected that these very different labelings share a common property, named Sense of Direction. In spite of the large amount of investigati ..."
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Cited by 32 (9 self)
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An extensive body of evidence exists of the impact that specific edge labelings have on the communication complexity of distributed problems. It has been long suspected that these very different labelings share a common property, named Sense of Direction. In spite of the large amount of investigations, and of the obvious practical importance, a formal characterization of this property did not exist. In this paper, we finally provide a formal definition of sense of direction, making explicit the very specific relationship between three factors: the labeling, the topological structure, and the local view that an entity has of the system. In a way, sense of direction is the capability of a node in the system to use the labeling to translate the local view of its neighbors into its own. Using the formal definition as an observational platform, we describe several properties which allow the translation process to be possible beyond the immediate neighborhood. Finally, we identify four gene...
Sense of Direction in Distributed Computing
 In 12th International Symposium on Distributed Computing (DISC
, 1998
"... Sense of Direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this pr ..."
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Cited by 27 (10 self)
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Sense of Direction is a property of labeled graphs which has been shown to have a definite impact on computability and complexity in systems of communicating entities, and whose applicability ranges from the analysis of graph classes to distributed object systems. The full consequences of this property are still not known; in fact, the ongoing investigations continue to bring new (often surprising) results, to establish unsuspected links with other research and/or application areas, and to pose more questions than they answer. The aim of this paper is to provide a view of the current status of research, describing some of the relevant results, and providing pointers to future research directions. 1 Introduction In its more general formulation, a distributed system is a collection of computational entities communicating by exchanging finite amounts of information, which we shall call messages. The exact nature of the entities (i.e., processors, processes, network nodes, agents,...
On the Impact of Sense of Direction on Message Complexity
 Information Processing Letters
, 1997
"... In this paper, we prove a general result on the impact of sense of direction. We show that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast, DepthFirst Traversal, Election, and Spanning Tree Const ..."
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Cited by 22 (8 self)
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In this paper, we prove a general result on the impact of sense of direction. We show that, in arbitrary graphs, any sense of direction has a dramatic effect on the communication complexity of several important distributed problems: Broadcast, DepthFirst Traversal, Election, and Spanning Tree Construction. In systems with n nodes and e communication links, the solution for the Depth First Traversal and the Broadcast problems require\Omega\Gamma e) messages with arbitrary labelings; we show that, with any sense of direction, they can be solved exchanging only \Theta(n) messages, even if the system is anonymous. The problems of Election and of SpanningTree Construction require \Omega\Gamma e + n log n) messages with arbitrary labelings; on the other hand, we show that they can be solved with \Theta(n log n) messages with any sense of direction. The results presented here completely explain and generalize the existing results which now follow as corollaries for specific labelings. K...
Linear Broadcasting and N log log N Election in Unoriented Hypercubes
, 1997
"... In this paper, we provide efficient broadcasting and election algorithms in unoriented hypercubes. First, O(N) broadcasting and traversing algorithms are introduced, where N is the number of hypercube vertices. This answers affirmatively the open question stated in [Tel95a] whether linearmessage b ..."
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Cited by 10 (2 self)
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In this paper, we provide efficient broadcasting and election algorithms in unoriented hypercubes. First, O(N) broadcasting and traversing algorithms are introduced, where N is the number of hypercube vertices. This answers affirmatively the open question stated in [Tel95a] whether linearmessage broadcasting and traversing can be achieved on hypercubes without sense of direction. Moreover, by exploiting new techniques we designed an O(N log log N) leader election algorithm. This is the first known solution being able to exploit graphtheoretic properties of unoriented hypercubes such that it outperforms algorithms designed for general graphs [GHS83].
On the Ádám Conjecture on Circulant Graphs
, 1998
"... We investigate the condition for isomorphism between circulant graphs which is known as the Adam property. We describe a wide class of graphs for which the Adam conjecture holds (and even in a stronger form refering to isospectrality rather than to isomorphism of graphs. In the important case of do ..."
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Cited by 9 (2 self)
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We investigate the condition for isomorphism between circulant graphs which is known as the Adam property. We describe a wide class of graphs for which the Adam conjecture holds (and even in a stronger form refering to isospectrality rather than to isomorphism of graphs. In the important case of double loop (circulant graphs of degree 4) we give an almost complete classification of all possible isospectral graphs. Such graphs arise in many applications including telecommunication networks, VLSI design and distributed computation and have been extensively studied in the literature. Our method is based on studying the graph spectra with the aid of some deep results of algebraic number theory. # Dept of Computing, MPCE, Macquarie University, Sydney, NSW 2109, Australia. bmans@mpce.mq.edu.au + Departimento di Matematica, Terza Universita delgi Studi, Largo S. L. Murialdo, 1, Roma, 00146, Italy. pappa@mat.uniroma3.it # Dept of Computing, MPCE, Macquarie University, Sydney, NSW 2109, Au...
DECONTAMINATING CHORDAL RINGS AND TORI USING MOBILE AGENTS
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
"... In this paper we consider a network where an intruder is moving “contaminating ” the nodes it passes by, and we focus on the problem of decontaminating such a network by a team of mobile agents. The contamination/decontamination process has the following asynchronous dynamics: when the team is depl ..."
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Cited by 9 (4 self)
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In this paper we consider a network where an intruder is moving “contaminating ” the nodes it passes by, and we focus on the problem of decontaminating such a network by a team of mobile agents. The contamination/decontamination process has the following asynchronous dynamics: when the team is deployed all nodes are assumed to be contaminated, when an agent transits on a node, it will clean the node, when the node is left with no agent, the node will be recontaminated as soon as at least one of its neighbours is contaminated. We study the problem in asynchronous chordal ring networks and in tori. We consider two variations of the model: one where agents have only local knowledge, the other in which they have “visibility”, i.e., they can “see ” the state of their neighbouring nodes. We first derive lower bounds on the minimum number of agents necessary for the decontamination. In the case of chordal rings we show that the number of agents necessary to perform the cleaning does not depend on the size of the network; in fact it is linear in the length of the longest chord (provided that it is not too long). In the case of a torus, the minimum number of agents is equal to 2 · h, where h is the smallest dimension. We then propose optimal strategies for decontamination and we analyse the number of moves and the time complexity of the decontamination algorithms, showing that the visibility assumption allows us to decrease substantially both complexity measures. Another advantage of the “visibility model ” is that agents move independently and autonomously without requiring any coordination.
Backward Consistency and Sense of Direction in Advanced Distributed Systems (Extended Abstract)
 IN PROC. OF THE 18TH A.C.M. SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 1999
"... The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the pointtopoint model and is realistic for systems where a communication link can connect only two entities. However, in ..."
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Cited by 7 (4 self)
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The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the pointtopoint model and is realistic for systems where a communication link can connect only two entities. However, in systems which use more advanced communication and interconnection technology such as buses, optical networks, wireless communication media, etc., and more importantly, heterogeneous systems (such as internet) which include any combination of the above, local orientation can not be assumed. In this paper we consider a new type of consistency which we shall call backward consistency and which, unlike sense of direction, can exist even without local orientation. Thus...
Optimal Irreversible Dynamos in Chordal Rings (Extended Abstract)
 in Proc.25th Workshop on GraphTheoretic Concepts in Computer Science – WG ’99, Lecture Notes in Computer Science
, 1999
"... ) P. Flocchini y F. Geurts z N. Santoro x Abstract We study the propagation of information in a network in the presence of irreversible faults to detect its dynamos, i.e. the patterns of initial faults which lead the entire system to fail by repeated and asynchronous application of a majorit ..."
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Cited by 6 (0 self)
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) P. Flocchini y F. Geurts z N. Santoro x Abstract We study the propagation of information in a network in the presence of irreversible faults to detect its dynamos, i.e. the patterns of initial faults which lead the entire system to fail by repeated and asynchronous application of a majority rule of each node on its neighbors' states. In our model, the network is a chordal ring. We establish lower and upper bounds on the number of initial faults of dynamos, and we fully characterize their structure for specic classes of chordal rings, namely weakly and strongly chorded rings. On top of consequences in distributed faulttolerant algorithms, the study of dynamos appears to model adequately the pollingbased decisionmaking process in social groups and the disease propagation among healthy bodies. Keywords: distributed computing, chordal ring, dynamo, majority rule, faulttolerance. 1 Introduction Let G be a simple connected graph where every node is colored either black or w...
On the dynamic initialization of parallel computers
 In Proc. of the 8th IEEE International Parallel Processing Symposium
, 1997
"... Abstract. The incremental and dynamic construction of interconnection networks from smaller components often leaves the fundamental problem of assigning addresses to processors to be contended with at powerup time. The problem is fundamental, for virtually all parallel algorithms known to the autho ..."
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Cited by 5 (2 self)
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Abstract. The incremental and dynamic construction of interconnection networks from smaller components often leaves the fundamental problem of assigning addresses to processors to be contended with at powerup time. The problem is fundamental, for virtually all parallel algorithms known to the authors assume that the processors know their global coordinates within the newly created entity. We refer to this problem as the initialization problem. Rather surprisingly, the initialization problem has not received much attention in the literature. Our main contribution is to present parallel algorithms for the initialization problem on a number of network topologies, including complete binary trees, meshes of trees, pyramids, linear arrays, rings, meshes, tori, higher dimensional meshes and tori, hypercubes, butterflies, linear arrays with a global bus, rings with a global bus and meshes with multiple broadcasting, under various assumptions about edge labels, leader existence, and a priori knowledge of the number of nodes in the network. With two exceptions, the proposed algorithms are optimal.
Optimal Elections in Faulty Loop Networks and Applications
 IEEE Transactions on Computers
, 1998
"... Loop networks (or Hamiltonian circulant graphs) are a popular class of faulttolerant network topologies which include rings and complete graphs. For this class, the fundamental problem of Leader Election has been extensively studied assuming either a faultfree system or an upperbound on the number ..."
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Cited by 4 (1 self)
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Loop networks (or Hamiltonian circulant graphs) are a popular class of faulttolerant network topologies which include rings and complete graphs. For this class, the fundamental problem of Leader Election has been extensively studied assuming either a faultfree system or an upperbound on the number of link failures. We consider loop networks where an arbitrary number of links has failed and a processor can only detect the status of its incident links. We show that a Leader Election protocol in a faulty loop network requires only O(n log n) messages in the worstcase, where n is the number of processors. Moreover, we show that this is optimal. The proposed algorithm also detects network partitions. We also show that it provides an optimal solution for arbitrary nonfaulty networks with sense of direction. keywords Loop Networks, Leader Election, FaultTolerance, Interconnection Networks, Distributed Algorithms, Sense of Direction. # This research supported in part by N.S.E.R.C, grant...