12,306 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Recent Advances in Fully Dynamic Graph Algorithms
In recent years, significant advances have been made in the design and
analysis of fully dynamic algorithms. However, these theoretical results have
received very little attention from the practical perspective. Few of the
algorithms are implemented and tested on real datasets, and their practical
potential is far from understood. Here, we present a quick reference guide to
recent engineering and theory results in the area of fully dynamic graph
algorithms
Stackelberg Max Closure with Multiple Followers
In a Stackelberg max closure game, we are given a digraph whose vertices correspond to projects from which firms can choose and whose arcs represent precedence constraints. Some projects are under the control of a leader who sets prices in the first stage of the game, while in the second stage, the firms choose a feasible subset of projects of maximum value. For a single follower, the leader’s problem of finding revenue-maximizing prices can be solved in strongly polynomial time. In this paper, we focus on the setting with multiple followers and distinguish two situations. In the case in which only one copy of each project is available (limited supply), we show that the two-follower problem is solvable in strongly polynomial time, whereas the problem with three or more followers is NP-hard. In the case of unlimited supply, that is, when sufficient copies of each project are available, we show that the two-follower problem is already APX-hard. As a side result, we prove that Stackelberg min vertex cover on bipartite graphs with a single follower is APX-hard
TAPER: query-aware, partition-enhancement for large, heterogenous, graphs
Graph partitioning has long been seen as a viable approach to address Graph
DBMS scalability. A partitioning, however, may introduce extra query processing
latency unless it is sensitive to a specific query workload, and optimised to
minimise inter-partition traversals for that workload. Additionally, it should
also be possible to incrementally adjust the partitioning in reaction to
changes in the graph topology, the query workload, or both. Because of their
complexity, current partitioning algorithms fall short of one or both of these
requirements, as they are designed for offline use and as one-off operations.
The TAPER system aims to address both requirements, whilst leveraging existing
partitioning algorithms. TAPER takes any given initial partitioning as a
starting point, and iteratively adjusts it by swapping chosen vertices across
partitions, heuristically reducing the probability of inter-partition
traversals for a given pattern matching queries workload. Iterations are
inexpensive thanks to time and space optimisations in the underlying support
data structures. We evaluate TAPER on two different large test graphs and over
realistic query workloads. Our results indicate that, given a hash-based
partitioning, TAPER reduces the number of inter-partition traversals by around
80%; given an unweighted METIS partitioning, by around 30%. These reductions
are achieved within 8 iterations and with the additional advantage of being
workload-aware and usable online.Comment: 12 pages, 11 figures, unpublishe
An extension of disjunctive programming and its impact for compact tree formulations
In the 1970’s, Balas [2, 4] introduced the concept of disjunctive programming, which is optimization over unions of polyhedra. One main result of his theory is that, given linear descriptions for each of the polyhedra to be taken in the union, one can easily derive an extended formulation of the convex hull of the union of these polyhedra. In this paper, we give a generalization of this result by extending the polyhedral structure of the variables coupling the polyhedra taken in the union. Using this generalized concept, we derive polynomial size linear programming formulations (compact formulations) of a well- known spanning tree approximation of Steiner trees and flow equivalent trees for node- as well as edge- capacitated undirected networks. We also present a compact formulation for Gomory-Hu trees, and, as a consequence, of the minimum T-cut problem (but not for the associated T-cut polyhedron). Recently, Kaibel and Loos [10] introduced a more involved framework called polyhedral branching systems to derive extended formulations. The most of our model can be expressed in terms of their framework. The value of our model can be seen in the fact that it completes their framework with an interesting algorithmic aspect.disjunctive programming, compact formulation, flow-equivalent trees, Gomory-Hu trees
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