44,939 research outputs found
Efficient Parallel Path Checking for Linear-Time Temporal Logic With Past and Bounds
Path checking, the special case of the model checking problem where the model
under consideration is a single path, plays an important role in monitoring,
testing, and verification. We prove that for linear-time temporal logic (LTL),
path checking can be efficiently parallelized. In addition to the core logic,
we consider the extensions of LTL with bounded-future (BLTL) and past-time
(LTL+Past) operators. Even though both extensions improve the succinctness of
the logic exponentially, path checking remains efficiently parallelizable: Our
algorithm for LTL, LTL+Past, and BLTL+Past is in AC^1(logDCFL) \subseteq NC
Simulating quantum computation by contracting tensor networks
The treewidth of a graph is a useful combinatorial measure of how close the
graph is to a tree. We prove that a quantum circuit with gates whose
underlying graph has treewidth can be simulated deterministically in
time, which, in particular, is polynomial in if
. Among many implications, we show efficient simulations for
log-depth circuits whose gates apply to nearby qubits only, a natural
constraint satisfied by most physical implementations. We also show that
one-way quantum computation of Raussendorf and Briegel (Physical Review
Letters, 86:5188--5191, 2001), a universal quantum computation scheme with
promising physical implementations, can be efficiently simulated by a
randomized algorithm if its quantum resource is derived from a small-treewidth
graph.Comment: 7 figure
Subexponential groups in 4-manifold topology
We present a new, more elementary proof of the Freedman-Teichner result that
the geometric classification techniques (surgery, s-cobordism, and
pseudoisotopy) hold for topological 4-manifolds with groups of subexponential
growth. In an appendix Freedman and Teichner give a correction to their
original proof, and reformulate the growth estimates in terms of coarse
geometry.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper14.abs.htm
Anytime coalition structure generation on synergy graphs
We consider the coalition structure generation (CSG) problem on synergy graphs, which arises in many practical applications where communication constraints, social or trust relationships must be taken into account when forming coalitions. We propose a novel representation of this problem based on the concept of edge contraction, and an innovative branch and bound approach (CFSS), which is particularly efficient when applied to a general class of characteristic functions. This new model provides a non-redundant partition of the search space, hence allowing an effective parallelisation. We evaluate CFSS on two benchmark functions, the edge sum with coordination cost and the collective energy purchasing functions, comparing its performance with the best algorithm for CSG on synergy graphs: DyCE. The latter approach is centralised and cannot be efficiently parallelised due to the exponential memory requirements in the number of agents, which limits its scalability (while CFSS memory requirements are only polynomial). Our results show that, when the graphs are very sparse, CFSS is 4 orders of magnitude faster than DyCE. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems (i.e., with more than 2700 agents
Algorithms for Graph-Constrained Coalition Formation in the Real World
Coalition formation typically involves the coming together of multiple,
heterogeneous, agents to achieve both their individual and collective goals. In
this paper, we focus on a special case of coalition formation known as
Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the
agents constrains the formation of coalitions. We focus on this type of problem
given that in many real-world applications, agents may be connected by a
communication network or only trust certain peers in their social network. We
propose a novel representation of this problem based on the concept of edge
contraction, which allows us to model the search space induced by the GCCF
problem as a rooted tree. Then, we propose an anytime solution algorithm
(CFSS), which is particularly efficient when applied to a general class of
characteristic functions called functions. Moreover, we show how CFSS can
be efficiently parallelised to solve GCCF using a non-redundant partition of
the search space. We benchmark CFSS on both synthetic and realistic scenarios,
using a real-world dataset consisting of the energy consumption of a large
number of households in the UK. Our results show that, in the best case, the
serial version of CFSS is 4 orders of magnitude faster than the state of the
art, while the parallel version is 9.44 times faster than the serial version on
a 12-core machine. Moreover, CFSS is the first approach to provide anytime
approximate solutions with quality guarantees for very large systems of agents
(i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press
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