7,196 research outputs found
Embedding cube-connected cycles graphs into faulty hypercubes
We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults
The Power of an Example: Hidden Set Size Approximation Using Group Queries and Conditional Sampling
We study a basic problem of approximating the size of an unknown set in a
known universe . We consider two versions of the problem. In both versions
the algorithm can specify subsets . In the first version, which
we refer to as the group query or subset query version, the algorithm is told
whether is non-empty. In the second version, which we refer to as the
subset sampling version, if is non-empty, then the algorithm receives
a uniformly selected element from . We study the difference between
these two versions under different conditions on the subsets that the algorithm
may query/sample, and in both the case that the algorithm is adaptive and the
case where it is non-adaptive. In particular we focus on a natural family of
allowed subsets, which correspond to intervals, as well as variants of this
family
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Parallel data compression
Data compression schemes remove data redundancy in communicated and stored data and increase the effective capacities of communication and storage devices. Parallel algorithms and implementations for textual data compression are surveyed. Related concepts from parallel computation and information theory are briefly discussed. Static and dynamic methods for codeword construction and transmission on various models of parallel computation are described. Included are parallel methods which boost system speed by coding data concurrently, and approaches which employ multiple compression techniques to improve compression ratios. Theoretical and empirical comparisons are reported and areas for future research are suggested
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