1,308 research outputs found
Solving the undirected feedback vertex set problem by local search
An undirected graph consists of a set of vertices and a set of undirected
edges between vertices. Such a graph may contain an abundant number of cycles,
then a feedback vertex set (FVS) is a set of vertices intersecting with each of
these cycles. Constructing a FVS of cardinality approaching the global minimum
value is a optimization problem in the nondeterministic polynomial-complete
complexity class, therefore it might be extremely difficult for some large
graph instances. In this paper we develop a simulated annealing local search
algorithm for the undirected FVS problem. By defining an order for the vertices
outside the FVS, we replace the global cycle constraints by a set of local
vertex constraints on this order. Under these local constraints the cardinality
of the focal FVS is then gradually reduced by the simulated annealing dynamical
process. We test this heuristic algorithm on large instances of Er\"odos-Renyi
random graph and regular random graph, and find that this algorithm is
comparable in performance to the belief propagation-guided decimation
algorithm.Comment: 6 page
Variable neighbourhood search for the minimum labelling Steiner tree problem
We present a study on heuristic solution approaches to the minimum labelling Steiner
tree problem, an NP-hard graph problem related to the minimum labelling spanning tree
problem. Given an undirected labelled connected graph, the aim is to find a spanning
tree covering a given subset of nodes of the graph, whose edges have the smallest number
of distinct labels. Such a model may be used to represent many real world problems in
telecommunications and multimodal transportation networks. Several metaheuristics are
proposed and evaluated. The approaches are compared to the widely adopted Pilot Method
and it is shown that the Variable Neighbourhood Search metaheuristic is the most effective
approach to the problem, obtaining high quality solutions in short computational running
times
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Variable neighbourhood search for the minimum labelling Steiner tree problem
We present a study on heuristic solution approaches to the minimum labelling Steiner tree problem, an NP-hard graph problem related to the minimum labelling spanning tree problem. Given an undirected labelled connected graph, the aim is to find a spanning tree covering a given subset of nodes of the graph, whose edges have the smallest number of distinct labels. Such a model may be used to represent many real world problems in telecommunications and multimodal transportation networks. Several metaheuristics are proposed and evaluated. The approaches are compared to the widely adopted Pilot Method and it is shown that the Variable Neighbourhood Search that we propose is the most effective metaheuristic for the problem, obtaining high quality solutions in short computational running time
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
QoS multicast tree construction in IP/DWDM optical internet by bio-inspired algorithms
Copyright @ Elsevier Ltd. All rights reserved.In this paper, two bio-inspired Quality of Service (QoS) multicast algorithms are proposed in IP over dense wavelength division multiplexing (DWDM) optical Internet. Given a QoS multicast request and the delay interval required by the application, both algorithms are able to find a flexible QoS-based cost suboptimal routing tree. They first construct the multicast trees based on ant colony optimization and artificial immune algorithm, respectively. Then a dedicated wavelength assignment algorithm is proposed to assign wavelengths to the trees aiming to minimize the delay of the wavelength conversion. In both algorithms, multicast routing and wavelength assignment are integrated into a single process. Therefore, they can find the multicast trees on which the least wavelength conversion delay is achieved. Load balance is also considered in both algorithms. Simulation results show that these two bio-inspired algorithms can construct high performance QoS routing trees for multicast applications in IP/DWDM optical Internet.This work was supported in part ny the Program for New Century Excellent Talents in University, the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1, the National Natural Science Foundation of China under Grant no. 60673159 and 70671020, the National High-Tech Reasearch and Development Plan of China under Grant no. 2007AA041201, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant no. 20070145017
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