18,373 research outputs found
Data-Collection for the Sloan Digital Sky Survey: a Network-Flow Heuristic
The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of
the entire sky, determining the positions and absolute brightnesses of more
than 100 million celestial objects''. The survey will be performed by taking
``snapshots'' through a large telescope. Each snapshot can capture up to 600
objects from a small circle of the sky. This paper describes the design and
implementation of the algorithm that is being used to determine the snapshots
so as to minimize their number. The problem is NP-hard in general; the
algorithm described is a heuristic, based on Lagriangian-relaxation and
min-cost network flow. It gets within 5-15% of a naive lower bound, whereas
using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete
Algorithms (1998
Partitioning networks into cliques: a randomized heuristic approach
In the context of community detection in social networks, the term community can be grounded in the strict way that simply everybody should know each other within the community. We consider the corresponding community detection problem. We search for a partitioning of a network into the minimum number of non-overlapping cliques, such that the cliques cover all vertices. This problem is called the clique covering problem (CCP) and is one of the classical NP-hard problems. For CCP, we propose a randomized heuristic approach. To construct a high quality solution to CCP, we present an iterated greedy (IG) algorithm. IG can also be combined with a heuristic used to determine how far the algorithm is from the optimum in the worst case. Randomized local search (RLS) for maximum independent set was proposed to find such a bound. The experimental results of IG and the bounds obtained by RLS indicate that IG is a very suitable technique for solving CCP in real-world graphs. In addition, we summarize our basic rigorous results, which were developed for analysis of IG and understanding of its behavior on several relevant graph classes
Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design
Heat exchanger network synthesis exploits excess heat by integrating process
hot and cold streams and improves energy efficiency by reducing utility usage.
Determining provably good solutions to the minimum number of matches is a
bottleneck of designing a heat recovery network using the sequential method.
This subproblem is an NP-hard mixed-integer linear program exhibiting
combinatorial explosion in the possible hot and cold stream configurations. We
explore this challenging optimization problem from a graph theoretic
perspective and correlate it with other special optimization problems such as
cost flow network and packing problems. In the case of a single temperature
interval, we develop a new optimization formulation without problematic big-M
parameters. We develop heuristic methods with performance guarantees using
three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy
packing. Numerical results from a collection of 51 instances substantiate the
strength of the methods
Statistical mechanics of the vertex-cover problem
We review recent progress in the study of the vertex-cover problem (VC). VC
belongs to the class of NP-complete graph theoretical problems, which plays a
central role in theoretical computer science. On ensembles of random graphs, VC
exhibits an coverable-uncoverable phase transition. Very close to this
transition, depending on the solution algorithm, easy-hard transitions in the
typical running time of the algorithms occur.
We explain a statistical mechanics approach, which works by mapping VC to a
hard-core lattice gas, and then applying techniques like the replica trick or
the cavity approach. Using these methods, the phase diagram of VC could be
obtained exactly for connectivities , where VC is replica symmetric.
Recently, this result could be confirmed using traditional mathematical
techniques. For , the solution of VC exhibits full replica symmetry
breaking.
The statistical mechanics approach can also be used to study analytically the
typical running time of simple complete and incomplete algorithms for VC.
Finally, we describe recent results for VC when studied on other ensembles of
finite- and infinite-dimensional graphs.Comment: review article, 26 pages, 9 figures, to appear in J. Phys. A: Math.
Ge
The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms
Evolutionary algorithms (EAs), a large class of general purpose optimization
algorithms inspired from the natural phenomena, are widely used in various
industrial optimizations and often show excellent performance. This paper
presents an attempt towards revealing their general power from a statistical
view of EAs. By summarizing a large range of EAs into the sampling-and-learning
framework, we show that the framework directly admits a general analysis on the
probable-absolute-approximate (PAA) query complexity. We particularly focus on
the framework with the learning subroutine being restricted as a binary
classification, which results in the sampling-and-classification (SAC)
algorithms. With the help of the learning theory, we obtain a general upper
bound on the PAA query complexity of SAC algorithms. We further compare SAC
algorithms with the uniform search in different situations. Under the
error-target independence condition, we show that SAC algorithms can achieve
polynomial speedup to the uniform search, but not super-polynomial speedup.
Under the one-side-error condition, we show that super-polynomial speedup can
be achieved. This work only touches the surface of the framework. Its power
under other conditions is still open
Insertion Heuristics for Central Cycle Problems
A central cycle problem requires a cycle that is
reasonably short and keeps a the maximum distance
from any node not on the cycle to its nearest
node on the cycle reasonably low. The objective
may be to minimise maximumdistance or cycle
length and the solution may have further constraints.
Most classes of central cycle problems
are NP-hard. This paper investigates insertion
heuristics for central cycle problems, drawing on
insertion heuristics for p-centres [7] and travelling
salesman tours [21]. It shows that a modified
farthest insertion heuristic has reasonable worstcase
bounds for a particular class of problem.
It then compares the performance of two farthest
insertion heuristics against each other and
against bounds (where available) obtained by integer
programming on a range of problems from
TSPLIB [20]. It shows that a simple farthest insertion
heuristic is fast, performs well in practice
and so is likely to be useful for a general problems
or as the basis for more complex heuristics
for specific problems
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