36,082 research outputs found
Graph Sparsification by Edge-Connectivity and Random Spanning Trees
We present new approaches to constructing graph sparsifiers --- weighted
subgraphs for which every cut has the same value as the original graph, up to a
factor of . Our first approach independently samples each
edge with probability inversely proportional to the edge-connectivity
between and . The fact that this approach produces a sparsifier resolves
a question posed by Bencz\'ur and Karger (2002). Concurrent work of Hariharan
and Panigrahi also resolves this question. Our second approach constructs a
sparsifier by forming the union of several uniformly random spanning trees.
Both of our approaches produce sparsifiers with
edges. Our proofs are based on extensions of Karger's contraction algorithm,
which may be of independent interest
Dynamic load balancing for the distributed mining of molecular structures
In molecular biology, it is often desirable to find common properties in large numbers of drug candidates. One family of
methods stems from the data mining community, where algorithms to find frequent graphs have received increasing attention over the
past years. However, the computational complexity of the underlying problem and the large amount of data to be explored essentially
render sequential algorithms useless. In this paper, we present a distributed approach to the frequent subgraph mining problem to
discover interesting patterns in molecular compounds. This problem is characterized by a highly irregular search tree, whereby no
reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely, a dynamic
partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiverinitiated
load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer
Institute’s HIV-screening data set, where we were able to show close-to linear speedup in a network of workstations. The proposed
approach also allows for dynamic resource aggregation in a non dedicated computational environment. These features make it suitable
for large-scale, multi-domain, heterogeneous environments, such as computational grids
Load-Balancing for Parallel Delaunay Triangulations
Computing the Delaunay triangulation (DT) of a given point set in
is one of the fundamental operations in computational geometry.
Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm
that merges two partial triangulations by re-triangulating a small subset of
their vertices - the border vertices - and combining the three triangulations
efficiently via parallel hash table lookups. The input point division should
therefore yield roughly equal-sized partitions for good load-balancing and also
result in a small number of border vertices for fast merging. In this paper, we
present a novel divide-step based on partitioning the triangulation of a small
sample of the input points. In experiments on synthetic and real-world data
sets, we achieve nearly perfectly balanced partitions and small border
triangulations. This almost cuts running time in half compared to
non-data-sensitive division schemes on inputs exhibiting an exploitable
underlying structure.Comment: Short version submitted to EuroPar 201
Faster Worst Case Deterministic Dynamic Connectivity
We present a deterministic dynamic connectivity data structure for undirected
graphs with worst case update time and constant query time. This improves on the previous best
deterministic worst case algorithm of Frederickson (STOC 1983) and Eppstein
Galil, Italiano, and Nissenzweig (J. ACM 1997), which had update time
. All other algorithms for dynamic connectivity are either
randomized (Monte Carlo) or have only amortized performance guarantees
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