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Practical Parallel Algorithms for Minimum Spanning Trees
 In Workshop on Advances in Parallel and Distributed Systems
, 1998
"... We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns ..."
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We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns are efficient, both in theory and in practice. The algorithms are evaluated theoretically using Valiant's BSP model of parallel computation and empirically through implementation results.
COST SHARING AND APPROXIMATION
, 2005
"... Central to this thesis are problems in which a group of users can benet from building and jointly using some kind of infrastructure, be it a set of supply depots, service stations, or a communication or transportation network. We study two important questions related to these kinds of scenarios: (1) ..."
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Central to this thesis are problems in which a group of users can benet from building and jointly using some kind of infrastructure, be it a set of supply depots, service stations, or a communication or transportation network. We study two important questions related to these kinds of scenarios: (1) how to build the shared facility that satises the needs of a given set of users in a costeective way, and (2) how to split the cost of the shared facility among the participating users in a fair and reasonable way. In the rst part of the thesis, we seek to design cost sharing functions with desirable gametheoretic properties. We are looking for cost sharing functions that are fair, and encourage cooperation among users. This is captured in the notion of crossmonotonicity: it says that a cost share of any user should never increase as more people join the system, and never decrease when players leave. Towards this end, we develop a new technique to generate such crossmonotonic cost shares using a primaldual type process, and use it to design crossmonotonic cost shares for several NPhard optimization problems.