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Coding advantage refers to the potential for network coding to improve end-to-end throughput or reduce routing cost. How large can the coding advantage be? We investigate this fundamental question in the classic undirected network model. So far, all known networks where such potential exists are based on a special class of topologies known as combinatorial networks. We try to prove a rather small...
It is shown that the problem of deciding and constructing a perfect matching in bipartite graphs G with the polynomial permanents of their n × n adjacency matrices A (perm(A) = nO(1)) are in the deterministic classes NC2 and NC3, respectively. We further design an NC3 algorithm for the problem of constructing all perfect matchings (enumeration problem) in a graph G with a permanent bounded by O(nk)...
Given a fixed set S of n keys, we would like to store them so that queries of the form "Is x ∈ S?" can be answered quickly. A commonly employed scheme to solve this problem uses a table to store the keys, and a special purpose program depending on S which probes the table. We analyze the tradeoff between the maximum number of probes allowable to answer a query, and the information-theoretic...
We study probabilistic on-line simulators for several machine models (or memory structures). The simulators have a more constrained access to data than the virtual machines, but are allowed to use probabilistic means to improve average access time. We show that in many cases coin tosses can not make up for inadequate access.
A general paradigm for relating measures of succinctness of representation and complexity theory is presented. The measures are based on the new Private and Blindfold Alternation machines. These measures are used to indicate the inherent information (or "randomness") of a string, but with respect to time and space complexity classes. These measures are then used to show that the existence...
We consider uniform circuit complexity, introduced by Borodin as a model of parallel complexity. Three main results are presented. First, we show that simultaneous size/depth of uniform circuits is the same as space/time of alternating Turing machines, with depth and time within a constant factor and likewise log(size) and space. Second, we apply this to characterize the class of polynomial size and...
A model of computation is introduced which permits the analysis of both the time and space requirements of non-oblivious programs. Using this model, it is demonstrated that any algorithm for sorting n inputs which is based on comparisons of individual inputs requires time-space product proportional to n2. Uniform and non-uniform sorting algorithms are presented which show that this lower bound is...
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