James Hegeman

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We study two fundamental graph problems, Graph Connectivity (GC) and Minimum Spanning Tree (MST), in the well-studied Congested Clique model, and present several new bounds on the time and message complexities of randomized algorithms for these problems. No non-trivial (i.e., super-constant) time lower bounds are known for either of the aforementioned(More)
The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed O(∆)-coloring algorithm running on the Congested Clique which has an expected running time of O(1) rounds, if ∆ ≥ Θ(log n); and(More)
This paper presents constant-time and near-constant-time distributed algorithms for a variety of problems in the congested clique model. We show how to compute a 3-ruling set in expected O(log log logn) rounds and using this, we obtain a constant-approximation to metric facility location, also in expected O(log log logn) rounds. In addition, assuming an(More)
This paper explores the design of “super-fast” distributed algorithms in settings in which bandwidth constraints impose severe restrictions on the volume of information that can quickly reach an individual node. As a starting point of our exploration, we consider networks of diameter one (i.e., cliques) so as to focus on bandwidth constraints only and avoid(More)
The facility location problem consists of a set of facilities F , a set of clients C, an opening cost fi associated with each facility xi, and a connection cost D(xi, yj) between each facility xi and client yj . The goal is to find a subset of facilities to open, and to connect each client to an open facility, so as to minimize the total facility opening(More)
The facility location problem consists of a set of facilities $${\mathcal {F}}$$ F , a set of clients $${\mathcal {C}}$$ C , an opening cost $$f_i$$ f i associated with each facility $$x_i$$ x i , and a connection cost $$D(x_i,y_j)$$ D ( x i , y j ) between each facility $$x_i$$ x i and client $$y_j$$ y j . The goal is to find a subset of facilities to(More)
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