Describes efficient sequential and parallel algorithms for orienting the edges of an undirected planar graph so that each vertex has few outgoing edges. From such an orientation one can test in constant time whether a given edge exists. One consequence is a parallel algorithm to list all subgraphs isomorphic to K3 or K4. More recently this paper has been cited for its applications to scheduling update operations in parallel finite element methods.
An earlier paper with Spiro at WADS 2009 provided dynamic graph algorithms for counting how many copies of each possible type of subgraph there are in a larger undirected graph, when the subgraphs have at most three vertices. This paper extends the method to directed graphs and to larger numbers of vertices per subgraph.
We investigate greedy routing schemes for social networks, in which participants know categorical information about some other participants and use it to guide message delivery by forwarding messages to neighbors that have more categories in common with the eventual destination. We define the membership dimension of such a scheme to be the maximum number of categories that any individual belongs to, a natural measure of the cognitive load of greedy routing on its participants. And we show that membership dimension is closely related to the small world phenomenon: a social network can be given a category system with polylogarithmic membership dimension that supports greedy routing if, and only if, the network has polylogarithmic diameter.
For several problems with polynomial-time solutions, we show that finding a sequence of steps that converts one solution into another (maintaining a valid solution at each step) is hard. These include planar monotone not-all-equal 3-sat, subset sum on integers of polynomial magnitude, and 0-1 integer programming with a constant number of linear inequality constraints.
Journals – Publications – David Eppstein – Theory Group – Inf. & Comp. Sci. – UC Irvine
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