29,863 research outputs found
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
Developing Efficient Metaheuristics for Communication Network Problems by using Problem-specific Knowledge
Metaheuristics, such as evolutionary algorithms or simulated annealing, are widely applicable heuristic optimization strategies that have shown encouraging results for a large number of difficult optimization problems. To show high performance, metaheuristics need to be adapted to the properties of the problem at hand. This paper illustrates how efficient metaheuristics can be developed for communication network problems by utilizing problem-specific knowledge for the design of a high-quality problem representation. The minimum communication spanning tree (MCST) problem finds a communication spanning tree that connects all nodes and satisfies their communication requirements for a minimum total cost. An investigation into the properties of the problem reveals that optimum solutions are similar to the minimum spanning tree (MST). Consequently, a problem-specific representation, the link biased (LB) encoding, is developed, which represents trees as a list of floats. The LB encoding makes use of the knowledge that optimum solutions are similar to the MST, and encodes trees that are similar to the MST with a higher probability. Experimental results for different types of metaheuristics show that metaheuristics using the LB-encoding efficiently solve existing MCST problem instances from the literature, as well as randomly generated MCST problems of different sizes and types
Dominators in Directed Graphs: A Survey of Recent Results, Applications, and Open Problems
The computation of dominators is a central tool in program optimization and code generation, and it has applications in other diverse areas includingconstraint programming, circuit testing, and biology. In this paper we survey recent results, applications, and open problems related to the notion of dominators in directed graphs,including dominator verification and certification, computing independent spanning trees, and connectivity and path-determination problems in directed graphs
Maximum Performance at Minimum Cost in Network Synchronization
We consider two optimization problems on synchronization of oscillator
networks: maximization of synchronizability and minimization of synchronization
cost. We first develop an extension of the well-known master stability
framework to the case of non-diagonalizable Laplacian matrices. We then show
that the solution sets of the two optimization problems coincide and are
simultaneously characterized by a simple condition on the Laplacian
eigenvalues. Among the optimal networks, we identify a subclass of hierarchical
networks, characterized by the absence of feedback loops and the normalization
of inputs. We show that most optimal networks are directed and
non-diagonalizable, necessitating the extension of the framework. We also show
how oriented spanning trees can be used to explicitly and systematically
construct optimal networks under network topological constraints. Our results
may provide insights into the evolutionary origin of structures in complex
networks for which synchronization plays a significant role.Comment: 29 pages, 9 figures, accepted for publication in Physica D, minor
correction
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