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Solving the minimum labelling spanning tree problem using hybrid local search
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum
labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest
number of distinct labels (or colours). In recent work, the MLST problem has been shown
to be NP-hard and some effective heuristics (Modified Genetic Algorithm (MGA) and Pilot
Method (PILOT)) have been proposed and analyzed. A hybrid local search method, that we
call Group-Swap Variable Neighbourhood Search (GS-VNS), is proposed in this paper. It is
obtained by combining two classic metaheuristics: Variable Neighbourhood Search (VNS) and
Simulated Annealing (SA). Computational experiments show that GS-VNS outperforms MGA
and PILOT. Furthermore, a comparison with the results provided by an exact approach shows
that we may quickly obtain optimal or near-optimal solutions with the proposed heuristic
zCap: a zero configuration adaptive paging and mobility management mechanism
Today, cellular networks rely on fixed collections of cells (tracking areas) for user equipment localisation. Locating users within these areas involves broadcast search (paging), which consumes radio bandwidth but reduces the user equipment signalling required for mobility management. Tracking areas are today manually configured, hard to adapt to local mobility and influence the load on several key resources in the network. We propose a decentralised and self-adaptive approach to mobility management based on a probabilistic model of local mobility. By estimating the parameters of this model from observations of user mobility collected online, we obtain a dynamic model from which we construct local neighbourhoods of cells where we are most likely to locate user equipment. We propose to replace the static tracking areas of current systems with neighbourhoods local to each cell. The model is also used to derive a multi-phase paging scheme, where the division of neighbourhood cells into consecutive phases balances response times and paging cost. The complete mechanism requires no manual tracking area configuration and performs localisation efficiently in terms of signalling and response times. Detailed simulations show that significant potential gains in localisation effi- ciency are possible while eliminating manual configuration of mobility management parameters. Variants of the proposal can be implemented within current (LTE) standards
Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search
Path planning in robotics often requires finding high-quality solutions to
continuously valued and/or high-dimensional problems. These problems are
challenging and most planning algorithms instead solve simplified
approximations. Popular approximations include graphs and random samples, as
respectively used by informed graph-based searches and anytime sampling-based
planners. Informed graph-based searches, such as A*, traditionally use
heuristics to search a priori graphs in order of potential solution quality.
This makes their search efficient but leaves their performance dependent on the
chosen approximation. If its resolution is too low then they may not find a
(suitable) solution but if it is too high then they may take a prohibitively
long time to do so. Anytime sampling-based planners, such as RRT*,
traditionally use random sampling to approximate the problem domain
incrementally. This allows them to increase resolution until a suitable
solution is found but makes their search dependent on the order of
approximation. Arbitrary sequences of random samples approximate the problem
domain in every direction simultaneously and but may be prohibitively
inefficient at containing a solution. This paper unifies and extends these two
approaches to develop Batch Informed Trees (BIT*), an informed, anytime
sampling-based planner. BIT* solves continuous path planning problems
efficiently by using sampling and heuristics to alternately approximate and
search the problem domain. Its search is ordered by potential solution quality,
as in A*, and its approximation improves indefinitely with additional
computational time, as in RRT*. It is shown analytically to be almost-surely
asymptotically optimal and experimentally to outperform existing sampling-based
planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16
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Heuristics based on greedy randomized adaptive search and variable neighbourhood search for the minimum labelling spanning tree problem
This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-complete. A Greedy Randomized Adaptive Search Procedure (GRASP) and different versions of Variable Neighbourhood Search (VNS) are proposed. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics
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