5,164 research outputs found
08431 Abstracts Collection -- Moderately Exponential Time Algorithms
From to , the Dagstuhl Seminar 08431 ``Moderately Exponential Time Algorithms \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
A fast Monte Carlo algorithm for site or bond percolation
We describe in detail a new and highly efficient algorithm for studying site
or bond percolation on any lattice. The algorithm can measure an observable
quantity in a percolation system for all values of the site or bond occupation
probability from zero to one in an amount of time which scales linearly with
the size of the system. We demonstrate our algorithm by using it to investigate
a number of issues in percolation theory, including the position of the
percolation transition for site percolation on the square lattice, the
stretched exponential behavior of spanning probabilities away from the critical
point, and the size of the giant component for site percolation on random
graphs.Comment: 17 pages, 13 figures. Corrections and some additional material in
this version. Accompanying material can be found on the web at
http://www.santafe.edu/~mark/percolation
Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme
We present and analyze a simple and general scheme to build a churn
(fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to
"convert" a static network into a dynamic distributed hash table(DHT)-based P2P
network such that all the good properties of the static network are guaranteed
with high probability (w.h.p). Applying our scheme to a cube-connected cycles
network, for example, yields a degree connected network, in which
every search succeeds in hops w.h.p., using messages,
where is the expected stable network size. Our scheme has an constant
storage overhead (the number of nodes responsible for servicing a data item)
and an overhead (messages and time) per insertion and essentially
no overhead for deletions. All these bounds are essentially optimal. While DHT
schemes with similar guarantees are already known in the literature, this work
is new in the following aspects:
(1) It presents a rigorous mathematical analysis of the scheme under a
general stochastic model of churn and shows the above guarantees;
(2) The theoretical analysis is complemented by a simulation-based analysis
that validates the asymptotic bounds even in moderately sized networks and also
studies performance under changing stable network size;
(3) The presented scheme seems especially suitable for maintaining dynamic
structures under churn efficiently. In particular, we show that a spanning tree
of low diameter can be efficiently maintained in constant time and logarithmic
number of messages per insertion or deletion w.h.p.
Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic
Analysis
QuickCast: Fast and Efficient Inter-Datacenter Transfers using Forwarding Tree Cohorts
Large inter-datacenter transfers are crucial for cloud service efficiency and
are increasingly used by organizations that have dedicated wide area networks
between datacenters. A recent work uses multicast forwarding trees to reduce
the bandwidth needs and improve completion times of point-to-multipoint
transfers. Using a single forwarding tree per transfer, however, leads to poor
performance because the slowest receiver dictates the completion time for all
receivers. Using multiple forwarding trees per transfer alleviates this
concern--the average receiver could finish early; however, if done naively,
bandwidth usage would also increase and it is apriori unclear how best to
partition receivers, how to construct the multiple trees and how to determine
the rate and schedule of flows on these trees. This paper presents QuickCast, a
first solution to these problems. Using simulations on real-world network
topologies, we see that QuickCast can speed up the average receiver's
completion time by as much as while only using more
bandwidth; further, the completion time for all receivers also improves by as
much as faster at high loads.Comment: [Extended Version] Accepted for presentation in IEEE INFOCOM 2018,
Honolulu, H
A time- and space-optimal algorithm for the many-visits TSP
The many-visits traveling salesperson problem (MV-TSP) asks for an optimal
tour of cities that visits each city a prescribed number of
times. Travel costs may be asymmetric, and visiting a city twice in a row may
incur a non-zero cost. The MV-TSP problem finds applications in scheduling,
geometric approximation, and Hamiltonicity of certain graph families.
The fastest known algorithm for MV-TSP is due to Cosmadakis and Papadimitriou
(SICOMP, 1984). It runs in time and
requires space. An interesting feature of the
Cosmadakis-Papadimitriou algorithm is its \emph{logarithmic} dependence on the
total length of the tour, allowing the algorithm to handle
instances with very long tours. The \emph{superexponential} dependence on the
number of cities in both the time and space complexity, however, renders the
algorithm impractical for all but the narrowest range of this parameter.
In this paper we improve upon the Cosmadakis-Papadimitriou algorithm, giving
an MV-TSP algorithm that runs in time , i.e.\
\emph{single-exponential} in the number of cities, using \emph{polynomial}
space. Our algorithm is deterministic, and arguably both simpler and easier to
analyse than the original approach of Cosmadakis and Papadimitriou. It involves
an optimization over directed spanning trees and a recursive, centroid-based
decomposition of trees.Comment: Small fixes, journal versio
A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles
Recent works have shown that quantum computers can polynomially speed up
certain SAT-solving algorithms even when the number of available qubits is
significantly smaller than the number of variables. Here we generalise this
approach. We present a framework for hybrid quantum-classical algorithms which
utilise quantum computers significantly smaller than the problem size. Given an
arbitrarily small ratio of the quantum computer to the instance size, we
achieve polynomial speedups for classical divide-and-conquer algorithms,
provided that certain criteria on the time- and space-efficiency are met. We
demonstrate how this approach can be used to enhance Eppstein's algorithm for
the cubic Hamiltonian cycle problem, and achieve a polynomial speedup for any
ratio of the number of qubits to the size of the graph.Comment: 20+2 page
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