55,696 research outputs found
Tightest Admissible Shortest Path
The shortest path problem in graphs is fundamental to AI. Nearly all variants
of the problem and relevant algorithms that solve them ignore edge-weight
computation time and its common relation to weight uncertainty. This implies
that taking these factors into consideration can potentially lead to a
performance boost in relevant applications. Recently, a generalized framework
for weighted directed graphs was suggested, where edge-weight can be computed
(estimated) multiple times, at increasing accuracy and run-time expense. We
build on this framework to introduce the problem of finding the tightest
admissible shortest path (TASP); a path with the tightest suboptimality bound
on the optimal cost. This is a generalization of the shortest path problem to
bounded uncertainty, where edge-weight uncertainty can be traded for
computational cost. We present a complete algorithm for solving TASP, with
guarantees on solution quality. Empirical evaluation supports the effectiveness
of this approach.Comment: arXiv admin note: text overlap with arXiv:2208.1148
Next Generation Cluster Editing
This work aims at improving the quality of structural variant prediction from
the mapped reads of a sequenced genome. We suggest a new model based on cluster
editing in weighted graphs and introduce a new heuristic algorithm that allows
to solve this problem quickly and with a good approximation on the huge graphs
that arise from biological datasets
The edge-disjoint path problem on random graphs by message-passing
We present a message-passing algorithm to solve the edge disjoint path
problem (EDP) on graphs incorporating under a unique framework both traffic
optimization and path length minimization. The min-sum equations for this
problem present an exponential computational cost in the number of paths. To
overcome this obstacle we propose an efficient implementation by mapping the
equations onto a weighted combinatorial matching problem over an auxiliary
graph. We perform extensive numerical simulations on random graphs of various
types to test the performance both in terms of path length minimization and
maximization of the number of accommodated paths. In addition, we test the
performance on benchmark instances on various graphs by comparison with
state-of-the-art algorithms and results found in the literature. Our
message-passing algorithm always outperforms the others in terms of the number
of accommodated paths when considering non trivial instances (otherwise it
gives the same trivial results). Remarkably, the largest improvement in
performance with respect to the other methods employed is found in the case of
benchmarks with meshes, where the validity hypothesis behind message-passing is
expected to worsen. In these cases, even though the exact message-passing
equations do not converge, by introducing a reinforcement parameter to force
convergence towards a sub optimal solution, we were able to always outperform
the other algorithms with a peak of 27% performance improvement in terms of
accommodated paths. On random graphs, we numerically observe two separated
regimes: one in which all paths can be accommodated and one in which this is
not possible. We also investigate the behaviour of both the number of paths to
be accommodated and their minimum total length.Comment: 14 pages, 8 figure
Edge Routing with Ordered Bundles
Edge bundling reduces the visual clutter in a drawing of a graph by uniting
the edges into bundles. We propose a method of edge bundling drawing each edge
of a bundle separately as in metro-maps and call our method ordered bundles. To
produce aesthetically looking edge routes it minimizes a cost function on the
edges. The cost function depends on the ink, required to draw the edges, the
edge lengths, widths and separations. The cost also penalizes for too many
edges passing through narrow channels by using the constrained Delaunay
triangulation. The method avoids unnecessary edge-node and edge-edge crossings.
To draw edges with the minimal number of crossings and separately within the
same bundle we develop an efficient algorithm solving a variant of the
metro-line crossing minimization problem. In general, the method creates clear
and smooth edge routes giving an overview of the global graph structure, while
still drawing each edge separately and thus enabling local analysis
Performance Models for Data Transfers: A Case Study with Molecular Chemistry Kernels
With increasing complexity of hardwares, systems with different memory nodes
are ubiquitous in High Performance Computing (HPC). It is paramount to develop
strategies to overlap the data transfers between memory nodes with computations
in order to exploit the full potential of these systems. In this article, we
consider the problem of deciding the order of data transfers between two memory
nodes for a set of independent tasks with the objective to minimize the
makespan. We prove that with limited memory capacity, obtaining the optimal
order of data transfers is a NP-complete problem. We propose several heuristics
for this problem and provide details about their favorable situations. We
present an analysis of our heuristics on traces, obtained by running 2
molecular chemistry kernels, namely, Hartree-Fock (HF) and Coupled Cluster
Single Double (CCSD) on 10 nodes of an HPC system. Our results show that some
of our heuristics achieve significant overlap for moderate memory capacities
and are very close to the lower bound of makespan
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