1,883 research outputs found
Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality
We consider the all pairs all shortest paths (APASP) problem, which maintains
the shortest path dag rooted at every vertex in a directed graph G=(V,E) with
positive edge weights. For this problem we present a decremental algorithm
(that supports the deletion of a vertex, or weight increases on edges incident
to a vertex). Our algorithm runs in amortized O(\vstar^2 \cdot \log n) time per
update, where n=|V|, and \vstar bounds the number of edges that lie on shortest
paths through any given vertex. Our APASP algorithm can be used for the
decremental computation of betweenness centrality (BC), a graph parameter that
is widely used in the analysis of large complex networks. No nontrivial
decremental algorithm for either problem was known prior to our work. Our
method is a generalization of the decremental algorithm of Demetrescu and
Italiano [DI04] for unique shortest paths, and for graphs with \vstar =O(n), we
match the bound in [DI04]. Thus for graphs with a constant number of shortest
paths between any pair of vertices, our algorithm maintains APASP and BC scores
in amortized time O(n^2 \log n) under decremental updates, regardless of the
number of edges in the graph.Comment: An extended abstract of this paper will appear in Proc. ISAAC 201
On-line construction of position heaps
We propose a simple linear-time on-line algorithm for constructing a position
heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap
differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it
considers the suffixes ordered from left to right. Our construction is based on
classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees
[Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into
the augmented position heap that allows for a linear-time string matching
algorithm [Ehrenfeucht et al, 2011].Comment: to appear in Journal of Discrete Algorithm
Drawing Graphs within Restricted Area
We study the problem of selecting a maximum-weight subgraph of a given graph
such that the subgraph can be drawn within a prescribed drawing area subject to
given non-uniform vertex sizes. We develop and analyze heuristics both for the
general (undirected) case and for the use case of (directed) calculation graphs
which are used to analyze the typical mistakes that high school students make
when transforming mathematical expressions in the process of calculating, for
example, sums of fractions
Localized Entanglement in one-dimensional Anderson model
The entanglement in one-dimensional Anderson model is studied. We show that
the pairwise entanglement measured by the average concurrence has a direct
relation to the localization length. The numerical study indicates that the
disorder significantly reduces the average entanglement, and entanglement
distribution clearly displays the entanglement localization. The maximal
pairwise entanglement exhibits a maximum as the disorder strength
increases,experiencing a transition from increase to decrease. The entanglement
between the center of localization and other site decreases exponentially along
the spatial direction. Finally,we study effects of disorder on dynamical
properties of entanglement.Comment: 5 pages, 6 figure
Ant colony optimisation and local search for bin-packing and cutting stock problems
The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO
Three-qubit pure-state canonical forms
In this paper we analyze the canonical forms into which any pure three-qubit
state can be cast. The minimal forms, i.e. the ones with the minimal number of
product states built from local bases, are also presented and lead to a
complete classification of pure three-qubit states. This classification is
related to the values of the polynomial invariants under local unitary
transformations by a one-to-one correspondence.Comment: REVTEX, 9 pages, 1 figur
On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games
In \emph{bandwidth allocation games} (BAGs), the strategy of a player
consists of various demands on different resources. The player's utility is at
most the sum of these demands, provided they are fully satisfied. Every
resource has a limited capacity and if it is exceeded by the total demand, it
has to be split between the players. Since these games generally do not have
pure Nash equilibria, we consider approximate pure Nash equilibria, in which no
player can improve her utility by more than some fixed factor through
unilateral strategy changes. There is a threshold (where
is a parameter that limits the demand of each player on a specific
resource) such that -approximate pure Nash equilibria always exist for
, but not for . We give both
upper and lower bounds on this threshold and show that the
corresponding decision problem is -hard. We also show that the
-approximate price of anarchy for BAGs is . For a restricted
version of the game, where demands of players only differ slightly from each
other (e.g. symmetric games), we show that approximate Nash equilibria can be
reached (and thus also be computed) in polynomial time using the best-response
dynamic. Finally, we show that a broader class of utility-maximization games
(which includes BAGs) converges quickly towards states whose social welfare is
close to the optimum
Quantum Correlations in Multipartite Quantum Systems
We review some concepts and properties of quantum correlations, in particular
multipartite measures, geometric measures and monogamy relations. We also
discuss the relation between classical and total correlationsComment: to be published as a chapter of the book "Lectures on general quantum
correlations and their applications" edited by F. Fanchini, D. Soares-Pinto,
and G. Adesso (Springer, 2017
Properties of Entanglement Monotones for Three-Qubit Pure States
Various parameterizations for the orbits under local unitary transformations
of three-qubit pure states are analyzed. The interconvertibility, symmetry
properties, parameter ranges, calculability and behavior under measurement are
looked at. It is shown that the entanglement monotones of any multipartite pure
state uniquely determine the orbit of that state under local unitary
transformations. It follows that there must be an entanglement monotone for
three-qubit pure states which depends on the Kempe invariant defined in [Phys.
Rev. A 60, 910 (1999)]. A form for such an entanglement monotone is proposed. A
theorem is proved that significantly reduces the number of entanglement
monotones that must be looked at to find the maximal probability of
transforming one multipartite state to another.Comment: 14 pages, REVTe
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