17,861 research outputs found
Phase Transitions and Computational Difficulty in Random Constraint Satisfaction Problems
We review the understanding of the random constraint satisfaction problems,
focusing on the q-coloring of large random graphs, that has been achieved using
the cavity method of the physicists. We also discuss the properties of the
phase diagram in temperature, the connections with the glass transition
phenomenology in physics, and the related algorithmic issues.Comment: 10 pages, Proceedings of the International Workshop on
Statistical-Mechanical Informatics 2007, Kyoto (Japan) September 16-19, 200
Joint Routing and STDMA-based Scheduling to Minimize Delays in Grid Wireless Sensor Networks
In this report, we study the issue of delay optimization and energy
efficiency in grid wireless sensor networks (WSNs). We focus on STDMA (Spatial
Reuse TDMA)) scheduling, where a predefined cycle is repeated, and where each
node has fixed transmission opportunities during specific slots (defined by
colors). We assume a STDMA algorithm that takes advantage of the regularity of
grid topology to also provide a spatially periodic coloring ("tiling" of the
same color pattern). In this setting, the key challenges are: 1) minimizing the
average routing delay by ordering the slots in the cycle 2) being energy
efficient. Our work follows two directions: first, the baseline performance is
evaluated when nothing specific is done and the colors are randomly ordered in
the STDMA cycle. Then, we propose a solution, ORCHID that deliberately
constructs an efficient STDMA schedule. It proceeds in two steps. In the first
step, ORCHID starts form a colored grid and builds a hierarchical routing based
on these colors. In the second step, ORCHID builds a color ordering, by
considering jointly both routing and scheduling so as to ensure that any node
will reach a sink in a single STDMA cycle. We study the performance of these
solutions by means of simulations and modeling. Results show the excellent
performance of ORCHID in terms of delays and energy compared to a shortest path
routing that uses the delay as a heuristic. We also present the adaptation of
ORCHID to general networks under the SINR interference model
Choosing Colors for Geometric Graphs via Color Space Embeddings
Graph drawing research traditionally focuses on producing geometric
embeddings of graphs satisfying various aesthetic constraints. After the
geometric embedding is specified, there is an additional step that is often
overlooked or ignored: assigning display colors to the graph's vertices. We
study the additional aesthetic criterion of assigning distinct colors to
vertices of a geometric graph so that the colors assigned to adjacent vertices
are as different from one another as possible. We formulate this as a problem
involving perceptual metrics in color space and we develop algorithms for
solving this problem by embedding the graph in color space. We also present an
application of this work to a distributed load-balancing visualization problem.Comment: 12 pages, 4 figures. To appear at 14th Int. Symp. Graph Drawing, 200
Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems
We introduce a generalization of the cavity, or Bethe-Peierls, method that
allows to follow Gibbs states when an external parameter, e.g. the temperature,
is adiabatically changed. This allows to obtain new quantitative results on the
static and dynamic behavior of mean field disordered systems such as models of
glassy and amorphous materials or random constraint satisfaction problems. As a
first application, we discuss the residual energy after a very slow annealing,
the behavior of out-of-equilibrium states, and demonstrate the presence of
temperature chaos in equilibrium. We also explore the energy landscape, and
identify a new transition from an computationally easier canyons-dominated
region to a harder valleys-dominated one.Comment: 6 pages, 7 figure
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