J-C. Bermond and D. Peleg. The Power of Small Coalitions in Graphs. Proc. 2nd Colloq. on Structural Information & Communication Complexity, Olympia, Greece, June 1995, Carleton Univ. Press, 173--184.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....i.e. dynamos. This is quite surprising considering that dynamos describe occurrences of faults which lead the entire system to a faulty behaviour. Most of the previous results were known in terms of monopolies, that is monotone dynamos which lead the system to an all black state in a single step [5, 3, 18]. Several related results were established in the study of catastrophic fault patterns for in nite chordal rings, that is, irreversible dynamos based on directional majority where a node becomes black if all its neighbours in the same direction are black [6, 17, 22] Recently, researchers have ....

J-C Bermond, D. Peleg. The power of small coalitions in graphs. In Proc. of 2nd Colloquium on Structural Information and Communication Complexity (SIROCCO 95), Olympia, 173-184, 1995.

.... are known in terms of catastrophic fault patterns which are dynamos based on one sided majority for infinite chordal rings (e.g. 5, 14, 19] Further results are known in the study of monopolies, which are the time constrainted version of dynamos: dynamos which converge in a single step [3, 4, 15]. Recently, some general lower and upper bounds on the size of monotone dynamos (i.e. dynamos where once a vertex becomes black, it never changes its colour) have been estabilished in [16] and a characterization of irreversible dynamos (i.e. dynamos in systems where the initial black vertices do ....

J-C Bermond, D. Peleg. The power of small coalitions in graphs. In Proc. of 2nd Colloquium on Structural Information and Communication Complexity, 173-184, 1995.

.... The lower bound for CCC comes from [13] found in terms of catastrophic fault patterns [5, 17, 22] Finer pointers to all the above literature can be found in [7] Further results are known in the study of monopolies, that is dynamos for which the system converges to all black in a single step [3, 4, 18]; and for monotone dinamos, that is configurations obeying reversible majority, where black vertices never turn white because a sufficiently large white neighbourhood never developes. Some lower and upper bounds on the size of monotone dynamos have been estabilished in [19] Irreversible dynamos ....

J-C Bermond and D. Peleg. The power of small coalitions in graphs. In Proc. of 2nd Colloquium on Structural Information and Communication Complexity (1995) 173-184.

....be irreversible; if instead the initial faults can be mended by the majority rule, the dynamo will be called reversible. Surprising, very little is known about dynamos. Most of the results are known for the static version of this process; that is, considering only a single step in the evolution [3, 5, 11, 18]. Recently, researchers have started to focus directly on dynamos. In particular, reversible monotone dynamos have been studied in general graphs [19] and tori [8] irreversible dynamos have been investigated in tori [7] butter y and similiar interconnection networks [12] In this paper we study ....

J.C. Bermond, D. Peleg. The power of small coalitions in graphs. In Proc. of 2nd Colloquium on Structural Information and Communication Complexity, 173-184. 1995.

....dynamos. Some results are known in terms of catastrophic fault patterns which are dynamos based on one sided majority for infinite chordal rings (e.g. 5, 14, 19] Further results are known in the study of monopolies, that is dynamos for which the system converges to all black in a single step [3, 4, 15]. Other more subtle definitions have been posed. An irreversible dynamo is one where the initial black vertices do not change their colour regardless of their neighbourhood. This is opposed to reversible dynamos, for which a vertex may switch colour several times according to a changing ....

J-C Bermond, D. Peleg. The power of small coalitions in graphs. In Proc. of 2nd Colloquium on Structural Information and Communication Complexity, 173-184, 1995.

No context found.

J-C. Bermond and D. Peleg. The Power of Small Coalitions in Graphs. Proc. 2nd Colloq. on Structural Information & Communication Complexity, Olympia, Greece, June 1995, Carleton Univ. Press, 173--184.

....every node stores information about its state at neighboring nodes. The obvious difficulty is that the data stored at a node for its neighbors might get corrupted just as easily as its own data. Moreover, simple voting schemes (if the node consults many neighbors) run into difficulties. See [KP95, LPRS93, P95]. We start by presenting a simplified solution for the case that jF j is known in advance. First we describe the local data structures D v employed in our solution. In addition to the output bit M v , each node v will store a bit D v (u) M u for each node u whose distance from v in the graph is ....

D. Peleg, The power of small Coalitions in graphs, Technical Report CS95-12, the Weizmann Institute of Science, 1995. (To appear in Proc. 2nd Colloq. on Structural Information & Communication Complexity, 1995.)

.... and lower bounds are provided for this problem, establishing that in an n vertex graph, an r monopoly M (for any even r 2) must be of size Omega Gamma n 3=5 ) and that for any r 2 there exist n vertex graphs with r monopolies of size O(n 3=5 ) This settles a problem left open in [LPRS93, BePe95]. 1 Introduction 1.1 The problem Majority voting, in one form or another, is used as a component of fault tolerant algorithms in a wide variety of contexts, including agreement and consensus problems (cf. LSP82, Brac87, DPPU88] quorum system applications (cf. Giff79, GMBa85, ObBe94, ....

....for even r 2 must be of size Omega Gamma n 3=5 ) 2. For any fixed r 2 there exist (infinitely many) n vertex graphs with r monopolies of size O(n 3=5 ) 1. 2 Related work The variant of a self ignoring r monopoly, namely, a set M that r controls every vertex in V n M was studied in [BePe95]. That paper also studied the influence of an arbitrary coalition M (that is not a monopoly) as a function of its size. Certain dynamic variants of majority voting problems were studied in the literature, in the context of discrete time dynamical systems. These variants dealt with a setting in ....

J-C. Bermond and D. Peleg. The Power of Small Coalitions in Graphs. 2nd SIROCCO, 1995.

....Mono (G; r) respectively, Psi Simon (G; r) denote the minimum cardinality of an r monopoly (resp. r SIMON) in G, Psi Mono (G; r) minfjM j : M V; Ruled(G; M; r) V g; Psi Simon (G; r) minfjM j : M V; Ruled(G; M; r) V n Mg: The following questions were addressed in [L 93, BP95, B 96] Q1) What is the maximum influence of a set M (as a function of jM j) namely, how many vertices can it possibly control (Q2) How small can a monopoly be (Q3) How small can a self ignoring monopoly be For 1 control, the example of Figure 1 gives us immediate answers to questions ....

.... Psi Mono (G; 1) Omega Gamma p n) 2. There exists a family of n vertex graphs G n with Psi Mono (G n ; 1) O( p n) Looking at r 2, it turns out that an extremal behavior similar to that of the example of Figure 1 may occur for r control as well, on certain graphs. Proposition 2. 2 [BP95] For any integer r 2 there exists a family of n vertex graphs G n such that Psi Ruled (G n ; r 1; r) n Gamma r Gamma 1) r. To illustrate this proposition, consider an integer r 2, and fix an integer p AE r and let n = rp (r 1) We now construct an n vertex graph G r;p in which a ....

[Article contains additional citation context not shown here]

J-C. Bermond and D. Peleg. The Power of Small Coalitions in Graphs. Proc. 2nd Colloq. on Structural Information & Communication Complexity, Olympia, Greece, June 1995, Carleton Univ. Press, 173--184.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC