751 research outputs found
Diameters, distortion and eigenvalues
We study the relation between the diameter, the first positive eigenvalue of
the discrete -Laplacian and the -distortion of a finite graph. We
prove an inequality relating these three quantities and apply it to families of
Cayley and Schreier graphs. We also show that the -distortion of Pascal
graphs, approximating the Sierpinski gasket, is bounded, which allows to obtain
estimates for the convergence to zero of the spectral gap as an application of
the main result.Comment: Final version, to appear in the European Journal of Combinatoric
Efficient Implementation of the Plan Graph in STAN
STAN is a Graphplan-based planner, so-called because it uses a variety of
STate ANalysis techniques to enhance its performance. STAN competed in the
AIPS-98 planning competition where it compared well with the other competitors
in terms of speed, finding solutions fastest to many of the problems posed.
Although the domain analysis techniques STAN exploits are an important factor
in its overall performance, we believe that the speed at which STAN solved the
competition problems is largely due to the implementation of its plan graph.
The implementation is based on two insights: that many of the graph
construction operations can be implemented as bit-level logical operations on
bit vectors, and that the graph should not be explicitly constructed beyond the
fix point. This paper describes the implementation of STAN's plan graph and
provides experimental results which demonstrate the circumstances under which
advantages can be obtained from using this implementation
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