19,182 research outputs found
The random K-satisfiability problem: from an analytic solution to an efficient algorithm
We study the problem of satisfiability of randomly chosen clauses, each with
K Boolean variables. Using the cavity method at zero temperature, we find the
phase diagram for the K=3 case. We show the existence of an intermediate phase
in the satisfiable region, where the proliferation of metastable states is at
the origin of the slowdown of search algorithms. The fundamental order
parameter introduced in the cavity method, which consists of surveys of local
magnetic fields in the various possible states of the system, can be computed
for one given sample. These surveys can be used to invent new types of
algorithms for solving hard combinatorial optimizations problems. One such
algorithm is shown here for the 3-sat problem, with very good performances.Comment: 38 pages, 13 figures; corrected typo
Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm
This paper explores optimization of paging and registration policies in
cellular networks. Motion is modeled as a discrete-time Markov process, and
minimization of the discounted, infinite-horizon average cost is addressed. The
structure of jointly optimal paging and registration policies is investigated
through the use of dynamic programming for partially observed Markov processes.
It is shown that there exist policies with a certain simple form that are
jointly optimal, though the dynamic programming approach does not directly
provide an efficient method to find the policies.
An iterative algorithm for policies with the simple form is proposed and
investigated. The algorithm alternates between paging policy optimization and
registration policy optimization. It finds a pair of individually optimal
policies, but an example is given showing that the policies need not be jointly
optimal. Majorization theory and Riesz's rearrangement inequality are used to
show that jointly optimal paging and registration policies are given for
symmetric or Gaussian random walk models by the nearest-location-first paging
policy and distance threshold registration policies.Comment: 13 pages, submitted to IEEE Trans. Information Theor
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