84,668 research outputs found
Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem
In the minimum common string partition (MCSP) problem two related input
strings are given. "Related" refers to the property that both strings consist
of the same set of letters appearing the same number of times in each of the
two strings. The MCSP seeks a minimum cardinality partitioning of one string
into non-overlapping substrings that is also a valid partitioning for the
second string. This problem has applications in bioinformatics e.g. in
analyzing related DNA or protein sequences. For strings with lengths less than
about 1000 letters, a previously published integer linear programming (ILP)
formulation yields, when solved with a state-of-the-art solver such as CPLEX,
satisfactory results. In this work, we propose a new, alternative ILP model
that is compared to the former one. While a polyhedral study shows the linear
programming relaxations of the two models to be equally strong, a comprehensive
experimental comparison using real-world as well as artificially created
benchmark instances indicates substantial computational advantages of the new
formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper
version replaces the one submitted on January 10, 2015, due to detected error
in the calculation of the variables involved in the ILP model
Internal Partitions of Regular Graphs
An internal partition of an -vertex graph is a partition of
such that every vertex has at least as many neighbors in its own part as in the
other part. It has been conjectured that every -regular graph with
vertices has an internal partition. Here we prove this for . The case
is of particular interest and leads to interesting new open problems on
cubic graphs. We also provide new lower bounds on and find new families
of graphs with no internal partitions. Weighted versions of these problems are
considered as well
Boolean Hedonic Games
We study hedonic games with dichotomous preferences. Hedonic games are
cooperative games in which players desire to form coalitions, but only care
about the makeup of the coalitions of which they are members; they are
indifferent about the makeup of other coalitions. The assumption of dichotomous
preferences means that, additionally, each player's preference relation
partitions the set of coalitions of which that player is a member into just two
equivalence classes: satisfactory and unsatisfactory. A player is indifferent
between satisfactory coalitions, and is indifferent between unsatisfactory
coalitions, but strictly prefers any satisfactory coalition over any
unsatisfactory coalition. We develop a succinct representation for such games,
in which each player's preference relation is represented by a propositional
formula. We show how solution concepts for hedonic games with dichotomous
preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic
and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen,
Norway, July 27-30, 201
Estimating good discrete partitions from observed data: symbolic false nearest neighbors
A symbolic analysis of observed time series data requires making a discrete
partition of a continuous state space containing observations of the dynamics.
A particular kind of partition, called ``generating'', preserves all dynamical
information of a deterministic map in the symbolic representation, but such
partitions are not obvious beyond one dimension, and existing methods to find
them require significant knowledge of the dynamical evolution operator or the
spectrum of unstable periodic orbits. We introduce a statistic and algorithm to
refine empirical partitions for symbolic state reconstruction. This method
optimizes an essential property of a generating partition: avoiding topological
degeneracies. It requires only the observed time series and is sensible even in
the presence of noise when no truly generating partition is possible. Because
of its resemblance to a geometrical statistic frequently used for
reconstructing valid time-delay embeddings, we call the algorithm ``symbolic
false nearest neighbors''
Use of available storage to improve scheduling in an automobile assembly plant
The Final Assembly Plant at General Motors-Holden's Automotive Ltd converts painted body shells into drive-away vehicles. It encounters difficulties when processing certain sequences of vehicles with high work contents, so GMHAL wishes to schedule its input to reduce or eliminate such undesirable sequences. GMHAL has a set of empirical rules for delineating undesirability.
The Painted Body Storage (PBS), which precedes Final Assembly, has 4 lanes that can be used to partially reschedule a vehicle sequence. Information on vehicle work content is available prior to arrival at the PBS, and GMHAL wants advice on using this data and the PBS to achieve a more satisfactory input to Final Assembly.
The Study Group devised three approaches.
1. Use the rules to show which short sequences are desirable and devise input and output strategies for the PBS to achieve these consistently. Choice between the strategies requires further investigation.
2. Model Final Assembly to produce an optimality criterion for vehicle sequences and use combinatorial optimization methods to optimise it over possible PBS outputs. A characterization of these outputs was derived.
3. Suggest that the initial production be suitably scheduled, which may substantially reduce the difficulties at the PBS stage
Existence of graphs with sub exponential transitions probability decay and applications
In this paper, we present a complete proof of the construction of graphs with
bounded valency such that the simple random walk has a return probability at
time at the origin of order for fixed and with Folner function . We begin
by giving a more detailled proof of this result contained in (see
\cite{ershdur}). In the second part, we give an application of the existence of
such graphs. We obtain bounds of the correct order for some functional of the
local time of a simple random walk on an infinite cluster on the percolation
model.Comment: 46 page
Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment
This paper presents a new optimal algorithm for locating a set of sensors in 3D able to see the boundaries of a polyhedral environment. Our approach is iterative and is based on a lower bound on the sensors' number and on a restriction of the original problem requiring each face to be observed in its entirety by at least one sensor. The lower bound allows evaluating the quality of the solution obtained at each step, and halting the algorithm if the solution is satisfactory. The algorithm asymptotically converges to the optimal solution of the unrestricted problem if the faces are subdivided into smaller part
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