55 research outputs found
Yet Another Graph Partitioning Problem is NP-Hard
Recently a large number of graph separator problems have been proven to be
\textsc{NP-Hard}. Amazingly we have found that
-Subgraph-Balanced-Vertex-Separator, an important variant, has been
overlooked. In this work ``Yet Another Graph Partitioning Problem is NP-Hard"
we present the surprising result that
-Subgraph-Balanced-Vertex-Separator is -Hard. This is despite the
fact that the constraints of our new problem are harder to satisfy than the
original problem
Partitioning Complex Networks via Size-constrained Clustering
The most commonly used method to tackle the graph partitioning problem in
practice is the multilevel approach. During a coarsening phase, a multilevel
graph partitioning algorithm reduces the graph size by iteratively contracting
nodes and edges until the graph is small enough to be partitioned by some other
algorithm. A partition of the input graph is then constructed by successively
transferring the solution to the next finer graph and applying a local search
algorithm to improve the current solution.
In this paper, we describe a novel approach to partition graphs effectively
especially if the networks have a highly irregular structure. More precisely,
our algorithm provides graph coarsening by iteratively contracting
size-constrained clusterings that are computed using a label propagation
algorithm. The same algorithm that provides the size-constrained clusterings
can also be used during uncoarsening as a fast and simple local search
algorithm.
Depending on the algorithm's configuration, we are able to compute partitions
of very high quality outperforming all competitors, or partitions that are
comparable to the best competitor in terms of quality, hMetis, while being
nearly an order of magnitude faster on average. The fastest configuration
partitions the largest graph available to us with 3.3 billion edges using a
single machine in about ten minutes while cutting less than half of the edges
than the fastest competitor, kMetis
Ensemble approach for generalized network dismantling
Finding a set of nodes in a network, whose removal fragments the network
below some target size at minimal cost is called network dismantling problem
and it belongs to the NP-hard computational class. In this paper, we explore
the (generalized) network dismantling problem by exploring the spectral
approximation with the variant of the power-iteration method. In particular, we
explore the network dismantling solution landscape by creating the ensemble of
possible solutions from different initial conditions and a different number of
iterations of the spectral approximation.Comment: 11 Pages, 4 Figures, 4 Table
FGPGA: An Efficient Genetic Approach for Producing Feasible Graph Partitions
Graph partitioning, a well studied problem of parallel computing has many
applications in diversified fields such as distributed computing, social
network analysis, data mining and many other domains. In this paper, we
introduce FGPGA, an efficient genetic approach for producing feasible graph
partitions. Our method takes into account the heterogeneity and capacity
constraints of the partitions to ensure balanced partitioning. Such approach
has various applications in mobile cloud computing that include feasible
deployment of software applications on the more resourceful infrastructure in
the cloud instead of mobile hand set. Our proposed approach is light weight and
hence suitable for use in cloud architecture. We ensure feasibility of the
partitions generated by not allowing over-sized partitions to be generated
during the initialization and search. Our proposed method tested on standard
benchmark datasets significantly outperforms the state-of-the-art methods in
terms of quality of partitions and feasibility of the solutions.Comment: Accepted in the 1st International Conference on Networking Systems
and Security 2015 (NSysS 2015
Advanced Multilevel Node Separator Algorithms
A node separator of a graph is a subset S of the nodes such that removing S
and its incident edges divides the graph into two disconnected components of
about equal size. In this work, we introduce novel algorithms to find small
node separators in large graphs. With focus on solution quality, we introduce
novel flow-based local search algorithms which are integrated in a multilevel
framework. In addition, we transfer techniques successfully used in the graph
partitioning field. This includes the usage of edge ratings tailored to our
problem to guide the graph coarsening algorithm as well as highly localized
local search and iterated multilevel cycles to improve solution quality even
further. Experiments indicate that flow-based local search algorithms on its
own in a multilevel framework are already highly competitive in terms of
separator quality. Adding additional local search algorithms further improves
solution quality. Our strongest configuration almost always outperforms
competing systems while on average computing 10% and 62% smaller separators
than Metis and Scotch, respectively
High-Quality Shared-Memory Graph Partitioning
Partitioning graphs into blocks of roughly equal size such that few edges run
between blocks is a frequently needed operation in processing graphs. Recently,
size, variety, and structural complexity of these networks has grown
dramatically. Unfortunately, previous approaches to parallel graph partitioning
have problems in this context since they often show a negative trade-off
between speed and quality. We present an approach to multi-level shared-memory
parallel graph partitioning that guarantees balanced solutions, shows high
speed-ups for a variety of large graphs and yields very good quality
independently of the number of cores used. For example, on 31 cores, our
algorithm partitions our largest test instance into 16 blocks cutting less than
half the number of edges than our main competitor when both algorithms are
given the same amount of time. Important ingredients include parallel label
propagation for both coarsening and improvement, parallel initial partitioning,
a simple yet effective approach to parallel localized local search, and fast
locality preserving hash tables
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