60,216 research outputs found
Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm
Motivated by the observation that FIFO-based push-relabel algorithms are able
to outperform highest label-based variants on modern, large maximum flow
problem instances, we introduce an efficient implementation of the algorithm
that uses coarse-grained parallelism to avoid the problems of existing parallel
approaches. We demonstrate good relative and absolute speedups of our algorithm
on a set of large graph instances taken from real-world applications. On a
modern 40-core machine, our parallel implementation outperforms existing
sequential implementations by up to a factor of 12 and other parallel
implementations by factors of up to 3
Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures
Quantum computers have recently made great strides and are on a long-term
path towards useful fault-tolerant computation. A dominant overhead in
fault-tolerant quantum computation is the production of high-fidelity encoded
qubits, called magic states, which enable reliable error-corrected computation.
We present the first detailed designs of hardware functional units that
implement space-time optimized magic-state factories for surface code
error-corrected machines. Interactions among distant qubits require surface
code braids (physical pathways on chip) which must be routed. Magic-state
factories are circuits comprised of a complex set of braids that is more
difficult to route than quantum circuits considered in previous work [1]. This
paper explores the impact of scheduling techniques, such as gate reordering and
qubit renaming, and we propose two novel mapping techniques: braid repulsion
and dipole moment braid rotation. We combine these techniques with graph
partitioning and community detection algorithms, and further introduce a
stitching algorithm for mapping subgraphs onto a physical machine. Our results
show a factor of 5.64 reduction in space-time volume compared to the best-known
previous designs for magic-state factories.Comment: 13 pages, 10 figure
Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Time
We give a nearly linear time randomized approximation scheme for the
Held-Karp bound [Held and Karp, 1970] for metric TSP. Formally, given an
undirected edge-weighted graph on edges and , the
algorithm outputs in time, with high probability, a
-approximation to the Held-Karp bound on the metric TSP instance
induced by the shortest path metric on . The algorithm can also be used to
output a corresponding solution to the Subtour Elimination LP. We substantially
improve upon the running time achieved previously
by Garg and Khandekar. The LP solution can be used to obtain a fast randomized
-approximation for metric TSP which improves
upon the running time of previous implementations of Christofides' algorithm
Heuristics for Network Coding in Wireless Networks
Multicast is a central challenge for emerging multi-hop wireless
architectures such as wireless mesh networks, because of its substantial cost
in terms of bandwidth. In this report, we study one specific case of multicast:
broadcasting, sending data from one source to all nodes, in a multi-hop
wireless network. The broadcast we focus on is based on network coding, a
promising avenue for reducing cost; previous work of ours showed that the
performance of network coding with simple heuristics is asymptotically optimal:
each transmission is beneficial to nearly every receiver. This is for
homogenous and large networks of the plan. But for small, sparse or for
inhomogeneous networks, some additional heuristics are required. This report
proposes such additional new heuristics (for selecting rates) for broadcasting
with network coding. Our heuristics are intended to use only simple local
topology information. We detail the logic of the heuristics, and with
experimental results, we illustrate the behavior of the heuristics, and
demonstrate their excellent performance
Adaptive Partitioning for Large-Scale Dynamic Graphs
Abstract—In 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
SAT Modulo Monotonic Theories
We define the concept of a monotonic theory and show how to build efficient
SMT (SAT Modulo Theory) solvers, including effective theory propagation and
clause learning, for such theories. We present examples showing that monotonic
theories arise from many common problems, e.g., graph properties such as
reachability, shortest paths, connected components, minimum spanning tree, and
max-flow/min-cut, and then demonstrate our framework by building SMT solvers
for each of these theories. We apply these solvers to procedural content
generation problems, demonstrating major speed-ups over state-of-the-art
approaches based on SAT or Answer Set Programming, and easily solving several
instances that were previously impractical to solve
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