Peter Winkler

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Let G be the digraph consisting of two oppositely-directed rings on the same set of n nodes. We provide a polynomialtime algorithm which, given a list of demands-each requiring a path from a specified source node to a specified target node-routes the demands so as to minimize the largest number of paths through any of the 2n directed links of G. The(More)
A graph G is given and two players, a cop and a robber, play the folioking game: the cop chooses a vertex, then the robber chooses a vertex, then the players move alternately beginning with the cop. A move consists of staying at one’s present vertex or moving to an adjacent vertex; each move is seen by both players. The cop wins if he manages to occupy the(More)
The following problem arose in the planning of optical communications networks which use bidirectional SONET rings. Traffic demands di,j are given for each pair of nodes in an n-node ring; each demand must be routed one of the two possible ways around the ring. The object is to minimize the maximum load on the cycle, where the load of an edge is the sum of(More)
17 There is one further consideration, which leads perhaps to the most intriguing conjecture of all. Let us put two tokens on a graph and let them take random walks, as before; but now suppose the schedule demon is clairvoyant|that is, he can see where each token will go, innnitely far into the future. The question is, with this advantage, can he now keep(More)
We model physical systems with ``hard constraints'' by the space Hom(G, H) of homomorphisms from a locally finite graph G to a fixed finite constraint graph H. For any assignment * of positive real activities to the nodes of H, there is at least one Gibbs measure on Hom(G, H); when G is infinite, there may be more than one. When G is a regular tree, the(More)
We model physical systems with \hard constraints" by the space Hom(G; H) of homomor-phisms from a locally nite graph G to a xed nite constraint graph H. Two homomorphisms are deemed to be adjacent if they diier on a single site of G. We investigate what appears to be a fundamental dichotomy of constraint graphs, by giving various characterizations of a(More)