98,414 research outputs found
Universal Cycles for Minimum Coverings of Pairs by Triples, with Application to 2-Radius Sequences
A new ordering, extending the notion of universal cycles of Chung {\em et
al.} (1992), is proposed for the blocks of -uniform set systems. Existence
of minimum coverings of pairs by triples that possess such an ordering is
established for all orders. Application to the construction of short 2-radius
sequences is given, with some new 2-radius sequences found through computer
search.Comment: 18 pages, to appear in Mathematics of Computatio
Convergence-Optimal Quantizer Design of Distributed Contraction-based Iterative Algorithms with Quantized Message Passing
In this paper, we study the convergence behavior of distributed iterative
algorithms with quantized message passing. We first introduce general iterative
function evaluation algorithms for solving fixed point problems distributively.
We then analyze the convergence of the distributed algorithms, e.g. Jacobi
scheme and Gauss-Seidel scheme, under the quantized message passing. Based on
the closed-form convergence performance derived, we propose two quantizer
designs, namely the time invariant convergence-optimal quantizer (TICOQ) and
the time varying convergence-optimal quantizer (TVCOQ), to minimize the effect
of the quantization error on the convergence. We also study the tradeoff
between the convergence error and message passing overhead for both TICOQ and
TVCOQ. As an example, we apply the TICOQ and TVCOQ designs to the iterative
waterfilling algorithm of MIMO interference game.Comment: 17 pages, 9 figures, Transaction on Signal Processing, accepte
The Advice Complexity of a Class of Hard Online Problems
The advice complexity of an online problem is a measure of how much knowledge
of the future an online algorithm needs in order to achieve a certain
competitive ratio. Using advice complexity, we define the first online
complexity class, AOC. The class includes independent set, vertex cover,
dominating set, and several others as complete problems. AOC-complete problems
are hard, since a single wrong answer by the online algorithm can have
devastating consequences. For each of these problems, we show that
bits of advice are
necessary and sufficient (up to an additive term of ) to achieve a
competitive ratio of .
The results are obtained by introducing a new string guessing problem related
to those of Emek et al. (TCS 2011) and B\"ockenhauer et al. (TCS 2014). It
turns out that this gives a powerful but easy-to-use method for providing both
upper and lower bounds on the advice complexity of an entire class of online
problems, the AOC-complete problems.
Previous results of Halld\'orsson et al. (TCS 2002) on online independent
set, in a related model, imply that the advice complexity of the problem is
. Our results improve on this by providing an exact formula for
the higher-order term. For online disjoint path allocation, B\"ockenhauer et
al. (ISAAC 2009) gave a lower bound of and an upper bound of
on the advice complexity. We improve on the upper bound by a
factor of . For the remaining problems, no bounds on their advice
complexity were previously known.Comment: Full paper to appear in Theory of Computing Systems. A preliminary
version appeared in STACS 201
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