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Lower Bounds for (Weak) Sense of Direction
 In Structure, Information and Communication Complexity. Proc. 7th Colloquium SIROCCO 2000, Proceedings In Informatics. Carleton Scientific
, 2000
"... A graph with n vertices and maximum degree # cannot be given weak sense of direction using less than # colours. It is known that n colours are always sufficient, but it has been conjectured that just #+1 are really needed. On the contrary, we show that for sufficiently large n there are graphs re ..."
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Cited by 2 (1 self)
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A graph with n vertices and maximum degree # cannot be given weak sense of direction using less than # colours. It is known that n colours are always sufficient, but it has been conjectured that just #+1 are really needed. On the contrary, we show that for sufficiently large n there are graphs
A Tool for Optimal Weak Sense of Direction
, 2000
"... Weak sense of direction is a property of the labelling of (possibly anonymous) networks that allows one to assign coherently local identifiers to other processors on the basis of the route followed by incoming messages. Though there exists a linear algorithm that allows one to assign a weak sense of ..."
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Weak sense of direction is a property of the labelling of (possibly anonymous) networks that allows one to assign coherently local identifiers to other processors on the basis of the route followed by incoming messages. Though there exists a linear algorithm that allows one to assign a weak sense
Weak Sense of Direction Labelings and Graph Embeddings
, 2010
"... An edgelabeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label sequences α and α ′ generated by nontrivial walks on G starting at u, f(α) = f(α ′ ) if and only if the two walks end at the ..."
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An edgelabeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label sequences α and α ′ generated by nontrivial walks on G starting at u, f(α) = f(α ′ ) if and only if the two walks end
A randomized protocol for signing contracts
, 1990
"... Two parties, A and B, want to sign a contract C over a communication network. To do so, they must “simultaneously” exchange their commitments to C. Since simultaneous exchange is usually impossible in practice, protocols are needed to approximate simultaneity by exchanging partial commitments in pie ..."
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Cited by 599 (11 self)
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in piece by piece manner. During such a protocol, one party or another may have a slight advantage; a “fair” protocol keeps this advantage within acceptable limits. We present a new protocol that is fair in the sense that, at any stage in its execution, the conditional probability that one party cannot
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a powerlaw (or if the coefficient sequence of f in a fixed basis decays like a power
Probabilistic checking of proofs: a new characterization of NP
 JOURNAL OF THE ACM
, 1998
"... We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof ..."
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Cited by 414 (26 self)
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the proof. We discuss implications of this characterization; specifically, we show that approximating Clique and Independent Set, even in a very weak sense, is NPhard.
More Lower Bounds for Weak Sense of Direction: The Case of Regular Graphs
"... A graph G with n vertices and maximum degree # G cannot be given weak sense of direction using less than # G colours. It is known that n colours are always sufficient, and it was conjectured that just # G + 1 are really needed, that is, one more colour is sufficient. Nonetheless, it has just been ..."
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Cited by 2 (0 self)
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A graph G with n vertices and maximum degree # G cannot be given weak sense of direction using less than # G colours. It is known that n colours are always sufficient, and it was conjectured that just # G + 1 are really needed, that is, one more colour is sufficient. Nonetheless, it has just been
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 456 (102 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely
NUMERICAL METHODS IN THE WEAK SENSE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH SMALL NOISE
"... Abstract. We propose a new approach to constructing weak numerical methods for nding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hi"j (h is a time increment, " is a small parameter). We derive various ecient weak sche ..."
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Abstract. We propose a new approach to constructing weak numerical methods for nding solutions to stochastic systems with small noise. For these methods we prove an error estimate in terms of products hi"j (h is a time increment, " is a small parameter). We derive various ecient weak
Results 1  10
of
3,443