18,236 research outputs found
Clique-Based Separators for Geometric Intersection Graphs
Let F be a set of n objects in the plane and let G^x(F) be its intersection graph. A balanced clique-based separator of G^x(F) is a set S consisting of cliques whose removal partitions G^x(F) into components of size at most δn, for some fixed constant δ < 1. The weight of a clique-based separator is defined as â_{C â S} log (|C|+1). Recently De Berg et al. (SICOMP 2020) proved that if S consists of convex fat objects, then G^x(F) admits a balanced clique-based separator of weight O(ân). We extend this result in several directions, obtaining the following results.
- Map graphs admit a balanced clique-based separator of weight O(ân), which is tight in the worst case.
- Intersection graphs of pseudo-disks admit a balanced clique-based separator of weight O(n^{2/3} log n). If the pseudo-disks are polygonal and of total complexity O(n) then the weight of the separator improves to O(ân log n).
- Intersection graphs of geodesic disks inside a simple polygon admit a balanced clique-based separator of weight O(n^{2/3} log n).
- Visibility-restricted unit-disk graphs in a polygonal domain with r reflex vertices admit a balanced clique-based separator of weight O(ân + r log(n/r)), which is tight in the worst case.
These results immediately imply sub-exponential algorithms for MAXIMUM INDEPENDENT SET (and, hence, VERTEX COVER), for FEEDBACK VERTEX SET, and for q-Coloring for constant q in these graph classes.ISSN:1868-896
Window-based Streaming Graph Partitioning Algorithm
In the recent years, the scale of graph datasets has increased to such a
degree that a single machine is not capable of efficiently processing large
graphs. Thereby, efficient graph partitioning is necessary for those large
graph applications. Traditional graph partitioning generally loads the whole
graph data into the memory before performing partitioning; this is not only a
time consuming task but it also creates memory bottlenecks. These issues of
memory limitation and enormous time complexity can be resolved using
stream-based graph partitioning. A streaming graph partitioning algorithm reads
vertices once and assigns that vertex to a partition accordingly. This is also
called an one-pass algorithm. This paper proposes an efficient window-based
streaming graph partitioning algorithm called WStream. The WStream algorithm is
an edge-cut partitioning algorithm, which distributes a vertex among the
partitions. Our results suggest that the WStream algorithm is able to partition
large graph data efficiently while keeping the load balanced across different
partitions, and communication to a minimum. Evaluation results with real
workloads also prove the effectiveness of our proposed algorithm, and it
achieves a significant reduction in load imbalance and edge-cut with different
ranges of dataset
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Adaptive Partitioning for Large-Scale Dynamic Graphs
AbstractâIn the last years, large-scale graph processing has gained increasing attention, with most recent systems placing particular emphasis on latency. One possible technique to improve runtime performance in a distributed graph processing system is to reduce network communication. The most notable way to achieve this goal is to partition the graph by minimizing the num-ber of edges that connect vertices assigned to different machines, while keeping the load balanced. However, real-world graphs are highly dynamic, with vertices and edges being constantly added and removed. Carefully updating the partitioning of the graph to reflect these changes is necessary to avoid the introduction of an extensive number of cut edges, which would gradually worsen computation performance. In this paper we show that performance degradation in dynamic graph processing systems can be avoided by adapting continuously the graph partitions as the graph changes. We present a novel highly scalable adaptive partitioning strategy, and show a number of refinements that make it work under the constraints of a large-scale distributed system. The partitioning strategy is based on iterative vertex migrations, relying only on local information. We have implemented the technique in a graph processing system, and we show through three real-world scenarios how adapting graph partitioning reduces execution time by over 50 % when compared to commonly used hash-partitioning. I
Exploiting Resolution-based Representations for MaxSAT Solving
Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver
in order to find an optimal solution. In particular, several algorithms take
advantage of the ability of SAT solvers to identify unsatisfiable subformulas.
Usually, these MaxSAT algorithms perform better when small unsatisfiable
subformulas are found early. However, this is not the case in many problem
instances, since the whole formula is given to the SAT solver in each call. In
this paper, we propose to partition the MaxSAT formula using a resolution-based
graph representation. Partitions are then iteratively joined by using a
proximity measure extracted from the graph representation of the formula. The
algorithm ends when only one partition remains and the optimal solution is
found. Experimental results show that this new approach further enhances a
state of the art MaxSAT solver to optimally solve a larger set of industrial
problem instances
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