9,143 research outputs found
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
Efficient Multi-Robot Coverage of a Known Environment
This paper addresses the complete area coverage problem of a known
environment by multiple-robots. Complete area coverage is the problem of moving
an end-effector over all available space while avoiding existing obstacles. In
such tasks, using multiple robots can increase the efficiency of the area
coverage in terms of minimizing the operational time and increase the
robustness in the face of robot attrition. Unfortunately, the problem of
finding an optimal solution for such an area coverage problem with multiple
robots is known to be NP-complete. In this paper we present two approximation
heuristics for solving the multi-robot coverage problem. The first solution
presented is a direct extension of an efficient single robot area coverage
algorithm, based on an exact cellular decomposition. The second algorithm is a
greedy approach that divides the area into equal regions and applies an
efficient single-robot coverage algorithm to each region. We present
experimental results for two algorithms. Results indicate that our approaches
provide good coverage distribution between robots and minimize the workload per
robot, meanwhile ensuring complete coverage of the area.Comment: In proceedings of IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS), 201
A General Large Neighborhood Search Framework for Solving Integer Programs
This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi
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