99,777 research outputs found
Label-connected graphs and the gossip problem
A graph with m edges is called label-connected if the edges can be labeled with real numbers in such a way that, for every pair (u, v) of vertices, there is a (u, v)-path with ascending labels. The minimum number of edges of a label-connected graph on n vertices equals the minimum number of calls in the gossip problem for n persons, which is known to be 2n − 4 for n ≥ 4. A polynomial characterization of label-connected graphs with n vertices and 2n − 4 edges is obtained. For a graph G, let θ(G) denote the minimum number of edges that have to be added to E(G) in order to create a graph with two edge-disjoint spanning trees. It is shown that for a graph G to be label-connected, θ(G) ≤ 2 is necessary and θ(G) ≤ 1 is sufficient. For i = 1, 2, the condition θ(G) ≤ i can be checked in polynomial time. Yet recognizing label-connected graphs is an NP-complete problem. This is established by first showing that the following problem is NP-complete: Given a graph G and two vertices u and v of G, does there exist a (u, v)-path P in G such that G−E(P) is connected
Fast Distributed Algorithms for LP-Type Problems of Bounded Dimension
In this paper we present various distributed algorithms for LP-type problems
in the well-known gossip model. LP-type problems include many important classes
of problems such as (integer) linear programming, geometric problems like
smallest enclosing ball and polytope distance, and set problems like hitting
set and set cover. In the gossip model, a node can only push information to or
pull information from nodes chosen uniformly at random. Protocols for the
gossip model are usually very practical due to their fast convergence, their
simplicity, and their stability under stress and disruptions. Our algorithms
are very efficient (logarithmic rounds or better with just polylogarithmic
communication work per node per round) whenever the combinatorial dimension of
the given LP-type problem is constant, even if the size of the given LP-type
problem is polynomially large in the number of nodes
Greedy Gossip with Eavesdropping
This paper presents greedy gossip with eavesdropping (GGE), a novel
randomized gossip algorithm for distributed computation of the average
consensus problem. In gossip algorithms, nodes in the network randomly
communicate with their neighbors and exchange information iteratively. The
algorithms are simple and decentralized, making them attractive for wireless
network applications. In general, gossip algorithms are robust to unreliable
wireless conditions and time varying network topologies. In this paper we
introduce GGE and demonstrate that greedy updates lead to rapid convergence. We
do not require nodes to have any location information. Instead, greedy updates
are made possible by exploiting the broadcast nature of wireless
communications. During the operation of GGE, when a node decides to gossip,
instead of choosing one of its neighbors at random, it makes a greedy
selection, choosing the node which has the value most different from its own.
In order to make this selection, nodes need to know their neighbors' values.
Therefore, we assume that all transmissions are wireless broadcasts and nodes
keep track of their neighbors' values by eavesdropping on their communications.
We show that the convergence of GGE is guaranteed for connected network
topologies. We also study the rates of convergence and illustrate, through
theoretical bounds and numerical simulations, that GGE consistently outperforms
randomized gossip and performs comparably to geographic gossip on
moderate-sized random geometric graph topologies.Comment: 25 pages, 7 figure
Exploiting the Synergy Between Gossiping and Structured Overlays
In this position paper we argue for exploiting the synergy between gossip-based algorithms and structured overlay networks (SON). These two strands of research have both aimed at building fault-tolerant, dynamic, self-managing, and large-scale distributed systems. Despite the common goals, the two areas have, however, been relatively isolated. We focus on three problem domains where there is an untapped potential of using gossiping combined with SONs. We argue for applying gossip-based membership for ring-based SONs---such as Chord and Bamboo---to make them handle partition mergers and loopy networks. We argue that small world SONs---such as Accordion and Mercury---are specifically well-suited for gossip-based membership management. The benefits would be better graph-theoretic properties. Finally, we argue that gossip-based algorithms could use the overlay constructed by SONs. For example, many unreliable broadcast algorithms for SONs could be augmented with anti-entropy protocols. Similarly, gossip-based aggregation could be used in SONs for network size estimation and load-balancing purposes
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