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- Gordon T. Wilfong, Peter Winkler
- SODA
- 1998

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)

- Richard J. Nowakowski, Peter Winkler
- Discrete Mathematics
- 1983

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)

- Peter Winkler
- Discrete Applied Mathematics
- 1984

- Graham R. Brightwell, Peter Winkler
- STOC
- 1991

We show that the problem of counting the number of linear extensions of a given partially ordered set is #P-complete. This settles a long-standing open question and contrssts with recent results giving randomized polynomial-time algorit hms for estimating the number of linear extensions. One consequence is that computing the volume of a rational polyhedron… (More)

- Alexander Schrijver, Paul D. Seymour, Peter Winkler
- SIAM J. Discrete Math.
- 1998

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)

- Don Coppersmith, Prasad Tetali, Peter Winkler
- SIAM J. Discrete Math.
- 1993

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)

- Graham R. Brightwell, Peter Winkler
- J. Comb. Theory, Ser. B
- 1999

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)

- Ronald Fagin, Moni Naor, Peter Winkler
- Commun. ACM
- 1996

We consider simple means by which two people may determine whether they possess the same information without revealing anything else to each other in case

- Graham R. Brightwell, Peter Winkler
- J. Comb. Theory, Ser. B
- 2000

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)

- Paul Erdös, Stephen Suen, Peter Winkler
- Random Struct. Algorithms
- 1995