1,929 research outputs found
The logic engine and the realization problem for nearest neighbor graphs
AbstractRoughly speaking, a “nearest neighbor graph” is formed from a set of points in the plane by joining two points if one is the nearest neighbor of the other. There are several ways in which this intuitive concept can be made precise.This paper investigates the complexity of determining whether, for a given graph G, there is a set of points P in the plane such that G is isomorphic to a nearest neighbor graph on P. We show that this problem is NP-hard for several definitions of nearest neighbor graph.Our proof technique uses an interesting simulation of a mechanical device called a “logic engine”
06481 Abstracts Collection -- Geometric Networks and Metric Space Embeddings
The Dagstuhl Seminar 06481 ``Geometric Networks and Metric Space
Embeddings\u27\u27 was held from November~26 to December~1, 2006 in the
International Conference and Research Center (IBFI), Schloss
Dagstuhl. During the seminar, several participants presented their
current research, and ongoing work and open problems were discussed.
In this paper we describe the seminar topics, we have compiled a
list of open questions that were posed during the seminar, there is
a list of all talks and there are abstracts of the presentations
given during the seminar. Links to extended abstracts or full
papers are provided where available
Localizability of Wireless Sensor Networks: Beyond Wheel Extension
A network is called localizable if the positions of all the nodes of the
network can be computed uniquely. If a network is localizable and embedded in
plane with generic configuration, the positions of the nodes may be computed
uniquely in finite time. Therefore, identifying localizable networks is an
important function. If the complete information about the network is available
at a single place, localizability can be tested in polynomial time. In a
distributed environment, networks with trilateration orderings (popular in real
applications) and wheel extensions (a specific class of localizable networks)
embedded in plane can be identified by existing techniques. We propose a
distributed technique which efficiently identifies a larger class of
localizable networks. This class covers both trilateration and wheel
extensions. In reality, exact distance is almost impossible or costly. The
proposed algorithm based only on connectivity information. It requires no
distance information
Setting Parameters by Example
We introduce a class of "inverse parametric optimization" problems, in which
one is given both a parametric optimization problem and a desired optimal
solution; the task is to determine parameter values that lead to the given
solution. We describe algorithms for solving such problems for minimum spanning
trees, shortest paths, and other "optimal subgraph" problems, and discuss
applications in multicast routing, vehicle path planning, resource allocation,
and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations
of Computer Science (FOCS '99
Two-Level Rectilinear Steiner Trees
Given a set of terminals in the plane and a partition of into
subsets , a two-level rectilinear Steiner tree consists of a
rectilinear Steiner tree connecting the terminals in each set
() and a top-level tree connecting the trees . The goal is to minimize the total length of all trees. This problem
arises naturally in the design of low-power physical implementations of parity
functions on a computer chip.
For bounded we present a polynomial time approximation scheme (PTAS) that
is based on Arora's PTAS for rectilinear Steiner trees after lifting each
partition into an extra dimension. For the general case we propose an algorithm
that predetermines a connection point for each and
().
Then, we apply any approximation algorithm for minimum rectilinear Steiner
trees in the plane to compute each and independently.
This gives us a -factor approximation with a running time of
suitable for fast practical computations. The
approximation factor reduces to by applying Arora's approximation scheme
in the plane
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