17,959 research outputs found
An O(n^{2.75}) algorithm for online topological ordering
We present a simple algorithm which maintains the topological order of a
directed acyclic graph with n nodes under an online edge insertion sequence in
O(n^{2.75}) time, independent of the number of edges m inserted. For dense
DAGs, this is an improvement over the previous best result of O(min(m^{3/2}
log(n), m^{3/2} + n^2 log(n)) by Katriel and Bodlaender. We also provide an
empirical comparison of our algorithm with other algorithms for online
topological sorting. Our implementation outperforms them on certain hard
instances while it is still competitive on random edge insertion sequences
leading to complete DAGs.Comment: 20 pages, long version of SWAT'06 pape
Correlated electron states and transport in triangular arrays
We study correlated electron states in frustrated geometry of a triangular
lattice. The interplay of long range interactions and finite residual entropy
of a classical system gives rise to unusual effects in equilibrium ordering as
well as in transport. A novel correlated fluid phase is identified in a wide
range of densities and temperatures above freezing into commensurate solid
phases. The charge dynamics in the correlated phase is described in terms of a
height field, its fluctuations, and topological defects. We demonstrate that
the height field fluctuations give rise to a ``free'' charge flow and finite dc
conductivity. We show that freezing into the solid phase, controlled by the
long range interactions, manifests itself in singularities of transport
properties.Comment: 19 pages, 10 figure
Fragmentation transition in a coevolving network with link-state dynamics
We study a network model that couples the dynamics of link states with the
evolution of the network topology. The state of each link, either A or B, is
updated according to the majority rule or zero-temperature Glauber dynamics, in
which links adopt the state of the majority of their neighboring links in the
network. Additionally, a link that is in a local minority is rewired to a
randomly chosen node. While large systems evolving under the majority rule
alone always fall into disordered topological traps composed by frustrated
links, any amount of rewiring is able to drive the network to complete order,
by relinking frustrated links and so releasing the system from traps. However,
depending on the relative rate of the majority rule and the rewiring processes,
the system evolves towards different ordered absorbing configurations: either a
one-component network with all links in the same state or a network fragmented
in two components with opposite states. For low rewiring rates and finite size
networks there is a domain of bistability between fragmented and non-fragmented
final states. Finite size scaling indicates that fragmentation is the only
possible scenario for large systems and any nonzero rate of rewiring.Comment: 10 pages, 13 figure
PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies
We develop the data structure PReaCH (for Pruned Reachability Contraction
Hierarchies) which supports reachability queries in a directed graph, i.e., it
supports queries that ask whether two nodes in the graph are connected by a
directed path. PReaCH adapts the contraction hierarchy speedup techniques for
shortest path queries to the reachability setting. The resulting approach is
surprisingly simple and guarantees linear space and near linear preprocessing
time. Orthogonally to that, we improve existing pruning techniques for the
search by gathering more information from a single DFS-traversal of the graph.
PReaCH-indices significantly outperform previous data structures with
comparable preprocessing cost. Methods with faster queries need significantly
more preprocessing time in particular for the most difficult instances
Online estimation of discrete densities using classifier chains
We propose an approach to estimate a discrete joint density online, that is, the algorithm is only provided the current example, its current estimate, and a limited amount of memory. To design an online estimator for discrete densities, we use classifier chains to model dependencies among features. Each classifier in the chain estimates the probability of one particular feature. Because a single chain may not provide a reliable estimate, we also consider ensembles of classifier chains. Our experiments on synthetic data show that the approach is feasible and the estimated densities approach the true, known distribution with increasing amounts of data
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