
Distributed Computation in the NodeCongested Clique
The Congested Clique model of distributed computing, which was introduce...
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Distributed Detection of Cliques in Dynamic Networks
This paper provides an indepth study of the fundamental problems of fin...
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Distributed Approximation Algorithms for Steiner Tree in the CONGESTED CLIQUE
The Steiner tree problem is one of the fundamental and classical problem...
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Random Sampling Applied to the MST Problem in the Node Congested Clique Model
The Congested Clique model, proposed by Lotker et al. [SPAA'03, SICOMP'0...
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Fast Neighborhood Rendezvous
In the rendezvous problem, two computing entities (called agents) locate...
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Approximate Neighbor Counting in Radio Networks
For many distributed algorithms, neighborhood size is an important param...
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Fast and Simple Deterministic Algorithms for HighlyDynamic Networks
This paper provides a surprisingly simple method for obtaining fast (con...
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Finding Subgraphs in Highly Dynamic Networks
In this paper we consider the fundamental problem of finding subgraphs in highly dynamic distributed networks  networks which allow an arbitrary number of links to be inserted / deleted per round. We show that the problems of kclique membership listing (for any k≥ 3), 4cycle listing and 5cycle listing can be deterministically solved in O(1)amortized round complexity, even with limited logarithmicsized messages. To achieve kclique membership listing we introduce a very useful combinatorial structure which we name the robust 2hop neighborhood. This is a subset of the 2hop neighborhood of a node, and we prove that it can be maintained in highly dynamic networks in O(1)amortized rounds. We also show that maintaining the actual 2hop neighborhood of a node requires near linear amortized time, showing the necessity of our definition. For 4cycle and 5cycle listing, we need edges within hop distance 3, for which we similarly define the robust 3hop neighborhood and prove it can be maintained in highly dynamic networks in O(1)amortized rounds. We complement the above with several impossibility results. We show that membership listing of any other graph on k≥ 3 nodes except kclique requires an almost linear number of amortized communication rounds. We also show that kcycle listing for k≥ 6 requires Ω(√(n) / log n) amortized rounds. This, combined with our upper bounds, paints a detailed picture of the complexity landscape for ultra fast graph finding algorithms in this highly dynamic environment.
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