1,699 research outputs found
GPU accelerated maximum cardinality matching algorithms for bipartite graphs
We design, implement, and evaluate GPU-based algorithms for the maximum
cardinality matching problem in bipartite graphs. Such algorithms have a
variety of applications in computer science, scientific computing,
bioinformatics, and other areas. To the best of our knowledge, ours is the
first study which focuses on GPU implementation of the maximum cardinality
matching algorithms. We compare the proposed algorithms with serial and
multicore implementations from the literature on a large set of real-life
problems where in majority of the cases one of our GPU-accelerated algorithms
is demonstrated to be faster than both the sequential and multicore
implementations.Comment: 14 pages, 5 figure
JGraphT -- A Java library for graph data structures and algorithms
Mathematical software and graph-theoretical algorithmic packages to
efficiently model, analyze and query graphs are crucial in an era where
large-scale spatial, societal and economic network data are abundantly
available. One such package is JGraphT, a programming library which contains
very efficient and generic graph data-structures along with a large collection
of state-of-the-art algorithms. The library is written in Java with stability,
interoperability and performance in mind. A distinctive feature of this library
is the ability to model vertices and edges as arbitrary objects, thereby
permitting natural representations of many common networks including
transportation, social and biological networks. Besides classic graph
algorithms such as shortest-paths and spanning-tree algorithms, the library
contains numerous advanced algorithms: graph and subgraph isomorphism; matching
and flow problems; approximation algorithms for NP-hard problems such as
independent set and TSP; and several more exotic algorithms such as Berge graph
detection. Due to its versatility and generic design, JGraphT is currently used
in large-scale commercial, non-commercial and academic research projects. In
this work we describe in detail the design and underlying structure of the
library, and discuss its most important features and algorithms. A
computational study is conducted to evaluate the performance of JGraphT versus
a number of similar libraries. Experiments on a large number of graphs over a
variety of popular algorithms show that JGraphT is highly competitive with
other established libraries such as NetworkX or the BGL.Comment: Major Revisio
Improved Bounds for Online Preemptive Matching
When designing a preemptive online algorithm for the maximum matching
problem, we wish to maintain a valid matching M while edges of the underlying
graph are presented one after the other. When presented with an edge e, the
algorithm should decide whether to augment the matching M by adding e (in which
case e may be removed later on) or to keep M in its current form without adding
e (in which case e is lost for good). The objective is to eventually hold a
matching M with maximum weight.
The main contribution of this paper is to establish new lower and upper
bounds on the competitive ratio achievable by preemptive online algorithms:
1. We provide a lower bound of 1+ln 2~1.693 on the competitive ratio of any
randomized algorithm for the maximum cardinality matching problem, thus
improving on the currently best known bound of e/(e-1)~1.581 due to Karp,
Vazirani, and Vazirani [STOC'90].
2. We devise a randomized algorithm that achieves an expected competitive
ratio of 5.356 for maximum weight matching. This finding demonstrates the power
of randomization in this context, showing how to beat the tight bound of 3
+2\sqrt{2}~5.828 for deterministic algorithms, obtained by combining the 5.828
upper bound of McGregor [APPROX'05] and the recent 5.828 lower bound of
Varadaraja [ICALP'11]
Two approximation algorithms for bipartite matching on multicore architectures
International audienceWe propose two heuristics for the bipartite matching problem that are amenable to shared-memory parallelization. The first heuristic is very intriguing from a parallelization perspective. It has no significant algorithmic synchronization overhead and no conflict resolution is needed across threads. We show that this heuristic has an approximation ratio of around 0.632 under some common conditions. The second heuristic is designed to obtain a larger matching by employing the well-known Karp-Sipser heuristic on a judiciously chosen subgraph of the original graph. We show that the Karp-Sipser heuristic always finds a maximum cardinality matching in the chosen subgraph. Although the Karp-Sipser heuristic is hard to parallelize for general graphs, we exploit the structure of the selected subgraphs to propose a specialized implementation which demonstrates very good scalability. We prove that this second heuristic has an approximation guarantee of around 0.866 under the same conditions as in the first algorithm. We discuss parallel implementations of the proposed heuristics on a multicore architecture. Experimental results, for demonstrating speed-ups and verifying the theoretical results in practice, are provided
Scalable Auction Algorithms for Bipartite Maximum Matching Problems
In this paper, we give new auction algorithms for maximum weighted bipartite
matching (MWM) and maximum cardinality bipartite -matching (MCbM). Our
algorithms run in and rounds, respectively, in the blackboard distributed
setting. We show that our MWM algorithm can be implemented in the distributed,
interactive setting using and bit messages,
respectively, directly answering the open question posed by Demange, Gale and
Sotomayor [DNO14]. Furthermore, we implement our algorithms in a variety of
other models including the the semi-streaming model, the shared-memory
work-depth model, and the massively parallel computation model. Our
semi-streaming MWM algorithm uses passes in space and our MCbM algorithm runs in
passes using space (where parameters represent
the degree constraints on the -matching and and represent the left
and right side of the bipartite graph, respectively). Both of these algorithms
improves \emph{exponentially} the dependence on in the space
complexity in the semi-streaming model against the best-known algorithms for
these problems, in addition to improvements in round complexity for MCbM.
Finally, our algorithms eliminate the large polylogarithmic dependence on
in depth and number of rounds in the work-depth and massively parallel
computation models, respectively, improving on previous results which have
large polylogarithmic dependence on (and exponential dependence on
in the MPC model).Comment: To appear in APPROX 202
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