6,035 research outputs found
Travelling on Graphs with Small Highway Dimension
We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP)
in graphs of low highway dimension. This graph parameter was introduced by
Abraham et al. [SODA 2010] as a model for transportation networks, on which TSP
and STP naturally occur for various applications in logistics. It was
previously shown [Feldmann et al. ICALP 2015] that these problems admit a
quasi-polynomial time approximation scheme (QPTAS) on graphs of constant
highway dimension. We demonstrate that a significant improvement is possible in
the special case when the highway dimension is 1, for which we present a
fully-polynomial time approximation scheme (FPTAS). We also prove that STP is
weakly NP-hard for these restricted graphs. For TSP we show NP-hardness for
graphs of highway dimension 6, which answers an open problem posed in [Feldmann
et al. ICALP 2015]
Distance Preserving Graph Simplification
Large graphs are difficult to represent, visualize, and understand. In this
paper, we introduce "gate graph" - a new approach to perform graph
simplification. A gate graph provides a simplified topological view of the
original graph. Specifically, we construct a gate graph from a large graph so
that for any "non-local" vertex pair (distance higher than some threshold) in
the original graph, their shortest-path distance can be recovered by
consecutive "local" walks through the gate vertices in the gate graph. We
perform a theoretical investigation on the gate-vertex set discovery problem.
We characterize its computational complexity and reveal the upper bound of
minimum gate-vertex set using VC-dimension theory. We propose an efficient
mining algorithm to discover a gate-vertex set with guaranteed logarithmic
bound. We further present a fast technique for pruning redundant edges in a
gate graph. The detailed experimental results using both real and synthetic
graphs demonstrate the effectiveness and efficiency of our approach.Comment: A short version of this paper will be published for ICDM'11, December
201
Towards Scalable Network Delay Minimization
Reduction of end-to-end network delays is an optimization task with
applications in multiple domains. Low delays enable improved information flow
in social networks, quick spread of ideas in collaboration networks, low travel
times for vehicles on road networks and increased rate of packets in the case
of communication networks. Delay reduction can be achieved by both improving
the propagation capabilities of individual nodes and adding additional edges in
the network. One of the main challenges in such design problems is that the
effects of local changes are not independent, and as a consequence, there is a
combinatorial search-space of possible improvements. Thus, minimizing the
cumulative propagation delay requires novel scalable and data-driven
approaches.
In this paper, we consider the problem of network delay minimization via node
upgrades. Although the problem is NP-hard, we show that probabilistic
approximation for a restricted version can be obtained. We design scalable and
high-quality techniques for the general setting based on sampling and targeted
to different models of delay distribution. Our methods scale almost linearly
with the graph size and consistently outperform competitors in quality
Random manifolds in non-linear resistor networks: Applications to varistors and superconductors
We show that current localization in polycrystalline varistors occurs on
paths which are, usually, in the universality class of the directed polymer in
a random medium. We also show that in ceramic superconductors, voltage
localizes on a surface which maps to an Ising domain wall. The emergence of
these manifolds is explained and their structure is illustrated using direct
solution of non-linear resistor networks
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