The authors study the question of determining whether an unknown function has a particular property or is /spl epsiv/-far from any function with that property. A property testing algorithm is given a sample of the val...
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The authors study the question of determining whether an unknown function has a particular property or is /spl epsiv/-far from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the function on instances of its choice. First, they establish some connections between property testing and problems in learning theory. Next, they focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being k-colorable or having a /spl rho/-clique (clique of density /spl rho/ w.r.t. the vertex set). The graph property testing algorithms are probabilistic and make assertions which are correct with high probability utilizing only poly(1//spl epsiv/) edge-queries into the graph, where /spl epsiv/ is the distance parameter. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph which correspond to the property being tested, if it holds for the input graph.
We show that no fixed number of parallel repetitions suffices in order to reduce the error in two-prover one-round proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz...
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We show that no fixed number of parallel repetitions suffices in order to reduce the error in two-prover one-round proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz (1995), showing that the number of rounds that suffice is inversely proportional to the answer length, are nearly best possible.
In »hot potato» packet routing problems, packets need to be routed to their respective destinations on a network. At each time step, each communication link can be traversed by at most one packet. Packets mu...
In this paper we consider a new type of cryptographic scheme, which can decode concealed images without any cryptographic computations. The scheme is perfectly secure and very easy to implement. We extend it into a vi...
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We present exact algorithms for finding a solution to the two-dimensional translational containment problem: find translations for k polygons which place them inside a polygonal container without overlApplng. We also ...
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ISBN:
(纸本)0898713498
We present exact algorithms for finding a solution to the two-dimensional translational containment problem: find translations for k polygons which place them inside a polygonal container without overlApplng. We also give an approximate algorithm: given any ϵ, it finds a set of translations such that no point of any polygon is more than 2ϵ inside the boundary of any other polygon or outside the container. The term &CN denotes a containment problem in which the κ polygons are convex and the container is nonconvex, and fcNN denotes nonconvex polygons and container. The polygons have up to m vertices, and the container has n vertices, where n > m (typically). We give exact algorithms for the following: 2CN in O(mnlogn) time, 3CN in O(m3ralogn) time, and ANN in O((mti)2κ+1LP(2κmn, + k2m2)) time, where LP(a, 6) is the time to solve a linear program with o variables and 6 constraints. We present an approximate algorithm for κNN whose running time is O((1/ϵ)κ log (1/ϵ)κ5slog s), where s is the largest number of vertices of any polygon that can generated by applying a certain set of operations to the input. We have no polynomial bound on s, but, in practice, it is usually not more than quadratic in n.
In "hot potato" packet routing problems, packets need to be routed to their respective destinations on a network. At each time step, each communication link can be traversed by at most one packet. Packets mu...
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In "hot potato" packet routing problems, packets need to be routed to their respective destinations on a network. At each time step, each communication link can be traversed by at most one packet. Packets must keep on moving until they reach their destinations, even if this means temporarily moving further away from their destinations. We investigate some simple design principles for hot potato routing algorithms. Perhaps our most important negative result is that for a wide class of natural algorithms, the number of deflections that a packet suffers can grow experimentally in the number of other packets in the network. On the positive side, we present some (admitedly weak) upper bounds on the worst case performance for algorithms for general networks, and for special cases such as the mesh, the torus, and the infinite line.< >
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