60,499 research outputs found
On Derandomizing Local Distributed Algorithms
The gap between the known randomized and deterministic local distributed
algorithms underlies arguably the most fundamental and central open question in
distributed graph algorithms. In this paper, we develop a generic and clean
recipe for derandomizing LOCAL algorithms. We also exhibit how this simple
recipe leads to significant improvements on a number of problem. Two main
results are:
- An improved distributed hypergraph maximal matching algorithm, improving on
Fischer, Ghaffari, and Kuhn [FOCS'17], and giving improved algorithms for
edge-coloring, maximum matching approximation, and low out-degree edge
orientation. The first gives an improved algorithm for Open Problem 11.4 of the
book of Barenboim and Elkin, and the last gives the first positive resolution
of their Open Problem 11.10.
- An improved distributed algorithm for the Lov\'{a}sz Local Lemma, which
gets closer to a conjecture of Chang and Pettie [FOCS'17], and moreover leads
to improved distributed algorithms for problems such as defective coloring and
-SAT.Comment: 37 page
Exponential Time Complexity of the Permanent and the Tutte Polynomial
We show conditional lower bounds for well-studied #P-hard problems:
(a) The number of satisfying assignments of a 2-CNF formula with n variables
cannot be counted in time exp(o(n)), and the same is true for computing the
number of all independent sets in an n-vertex graph.
(b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed
in time exp(o(n)).
(c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time
exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it
cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs.
Our lower bounds are relative to (variants of) the Exponential Time
Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF
formulas cannot be decided in time exp(o(n)). We relax this hypothesis by
introducing its counting version #ETH, namely that the satisfying assignments
cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds,
we transfer the sparsification lemma for d-CNF formulas to the counting
setting
Complexity Measures from Interaction Structures
We evaluate new complexity measures on the symbolic dynamics of coupled tent
maps and cellular automata. These measures quantify complexity in terms of
-th order statistical dependencies that cannot be reduced to interactions
between units. We demonstrate that these measures are able to identify
complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex
A note on uniform power connectivity in the SINR model
In this paper we study the connectivity problem for wireless networks under
the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio
transmitters distributed in some area, we seek to build a directed strongly
connected communication graph, and compute an edge coloring of this graph such
that the transmitter-receiver pairs in each color class can communicate
simultaneously. Depending on the interference model, more or less colors,
corresponding to the number of frequencies or time slots, are necessary. We
consider the SINR model that compares the received power of a signal at a
receiver to the sum of the strength of other signals plus ambient noise . The
strength of a signal is assumed to fade polynomially with the distance from the
sender, depending on the so-called path-loss exponent .
We show that, when all transmitters use the same power, the number of colors
needed is constant in one-dimensional grids if as well as in
two-dimensional grids if . For smaller path-loss exponents and
two-dimensional grids we prove upper and lower bounds in the order of
and for and
for respectively. If nodes are distributed
uniformly at random on the interval , a \emph{regular} coloring of
colors guarantees connectivity, while colors are required for any coloring.Comment: 13 page
Cutset Sampling for Bayesian Networks
The paper presents a new sampling methodology for Bayesian networks that
samples only a subset of variables and applies exact inference to the rest.
Cutset sampling is a network structure-exploiting application of the
Rao-Blackwellisation principle to sampling in Bayesian networks. It improves
convergence by exploiting memory-based inference algorithms. It can also be
viewed as an anytime approximation of the exact cutset-conditioning algorithm
developed by Pearl. Cutset sampling can be implemented efficiently when the
sampled variables constitute a loop-cutset of the Bayesian network and, more
generally, when the induced width of the networks graph conditioned on the
observed sampled variables is bounded by a constant w. We demonstrate
empirically the benefit of this scheme on a range of benchmarks
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