25,097 research outputs found
Metrical Service Systems with Multiple Servers
We study the problem of metrical service systems with multiple servers
(MSSMS), which generalizes two well-known problems -- the -server problem,
and metrical service systems. The MSSMS problem is to service requests, each of
which is an -point subset of a metric space, using servers, with the
objective of minimizing the total distance traveled by the servers.
Feuerstein initiated a study of this problem by proving upper and lower
bounds on the deterministic competitive ratio for uniform metric spaces. We
improve Feuerstein's analysis of the upper bound and prove that his algorithm
achieves a competitive ratio of . In the randomized
online setting, for uniform metric spaces, we give an algorithm which achieves
a competitive ratio , beating the deterministic lower
bound of . We prove that any randomized algorithm for
MSSMS on uniform metric spaces must be -competitive. We then
prove an improved lower bound of on
the competitive ratio of any deterministic algorithm for -MSSMS, on
general metric spaces. In the offline setting, we give a pseudo-approximation
algorithm for -MSSMS on general metric spaces, which achieves an
approximation ratio of using servers. We also prove a matching
hardness result, that a pseudo-approximation with less than servers is
unlikely, even for uniform metric spaces. For general metric spaces, we
highlight the limitations of a few popular techniques, that have been used in
algorithm design for the -server problem and metrical service systems.Comment: 18 pages; accepted for publication at COCOON 201
Property-Driven Fence Insertion using Reorder Bounded Model Checking
Modern architectures provide weaker memory consistency guarantees than
sequential consistency. These weaker guarantees allow programs to exhibit
behaviours where the program statements appear to have executed out of program
order. Fortunately, modern architectures provide memory barriers (fences) to
enforce the program order between a pair of statements if needed. Due to the
intricate semantics of weak memory models, the placement of fences is
challenging even for experienced programmers. Too few fences lead to bugs
whereas overuse of fences results in performance degradation. This motivates
automated placement of fences. Tools that restore sequential consistency in the
program may insert more fences than necessary for the program to be correct.
Therefore, we propose a property-driven technique that introduces
"reorder-bounded exploration" to identify the smallest number of program
locations for fence placement. We implemented our technique on top of CBMC;
however, in principle, our technique is generic enough to be used with any
model checker. Our experimental results show that our technique is faster and
solves more instances of relevant benchmarks as compared to earlier approaches.Comment: 18 pages, 3 figures, 4 algorithms. Version change reason : new set of
results and publication ready version of FM 201
Quantum walks on quotient graphs
A discrete-time quantum walk on a graph is the repeated application of a
unitary evolution operator to a Hilbert space corresponding to the graph. If
this unitary evolution operator has an associated group of symmetries, then for
certain initial states the walk will be confined to a subspace of the original
Hilbert space. Symmetries of the original graph, given by its automorphism
group, can be inherited by the evolution operator. We show that a quantum walk
confined to the subspace corresponding to this symmetry group can be seen as a
different quantum walk on a smaller quotient graph. We give an explicit
construction of the quotient graph for any subgroup of the automorphism group
and illustrate it with examples. The automorphisms of the quotient graph which
are inherited from the original graph are the original automorphism group
modulo the subgroup used to construct it. We then analyze the behavior of
hitting times on quotient graphs. Hitting time is the average time it takes a
walk to reach a given final vertex from a given initial vertex. It has been
shown in earlier work [Phys. Rev. A {\bf 74}, 042334 (2006)] that the hitting
time can be infinite. We give a condition which determines whether the quotient
graph has infinite hitting times given that they exist in the original graph.
We apply this condition for the examples discussed and determine which quotient
graphs have infinite hitting times. All known examples of quantum walks with
fast hitting times correspond to systems with quotient graphs much smaller than
the original graph; we conjecture that the existence of a small quotient graph
with finite hitting times is necessary for a walk to exhibit a quantum
speed-up.Comment: 18 pages, 7 figures in EPS forma
Communication Primitives in Cognitive Radio Networks
Cognitive radio networks are a new type of multi-channel wireless network in
which different nodes can have access to different sets of channels. By
providing multiple channels, they improve the efficiency and reliability of
wireless communication. However, the heterogeneous nature of cognitive radio
networks also brings new challenges to the design and analysis of distributed
algorithms.
In this paper, we focus on two fundamental problems in cognitive radio
networks: neighbor discovery, and global broadcast. We consider a network
containing nodes, each of which has access to channels. We assume the
network has diameter , and each pair of neighbors have at least ,
and at most , shared channels. We also assume each node has at
most neighbors. For the neighbor discovery problem, we design a
randomized algorithm CSeek which has time complexity
. CSeek is flexible and robust,
which allows us to use it as a generic "filter" to find "well-connected"
neighbors with an even shorter running time. We then move on to the global
broadcast problem, and propose CGCast, a randomized algorithm which takes
time. CGCast uses
CSeek to achieve communication among neighbors, and uses edge coloring to
establish an efficient schedule for fast message dissemination.
Towards the end of the paper, we give lower bounds for solving the two
problems. These lower bounds demonstrate that in many situations, CSeek and
CGCast are near optimal
RRR: Rank-Regret Representative
Selecting the best items in a dataset is a common task in data exploration.
However, the concept of "best" lies in the eyes of the beholder: different
users may consider different attributes more important, and hence arrive at
different rankings. Nevertheless, one can remove "dominated" items and create a
"representative" subset of the data set, comprising the "best items" in it. A
Pareto-optimal representative is guaranteed to contain the best item of each
possible ranking, but it can be almost as big as the full data. Representative
can be found if we relax the requirement to include the best item for every
possible user, and instead just limit the users' "regret". Existing work
defines regret as the loss in score by limiting consideration to the
representative instead of the full data set, for any chosen ranking function.
However, the score is often not a meaningful number and users may not
understand its absolute value. Sometimes small ranges in score can include
large fractions of the data set. In contrast, users do understand the notion of
rank ordering. Therefore, alternatively, we consider the position of the items
in the ranked list for defining the regret and propose the {\em rank-regret
representative} as the minimal subset of the data containing at least one of
the top- of any possible ranking function. This problem is NP-complete. We
use the geometric interpretation of items to bound their ranks on ranges of
functions and to utilize combinatorial geometry notions for developing
effective and efficient approximation algorithms for the problem. Experiments
on real datasets demonstrate that we can efficiently find small subsets with
small rank-regrets
Constant-Factor Approximation for TSP with Disks
We revisit the traveling salesman problem with neighborhoods (TSPN) and
present the first constant-ratio approximation for disks in the plane: Given a
set of disks in the plane, a TSP tour whose length is at most times
the optimal can be computed in time that is polynomial in . Our result is
the first constant-ratio approximation for a class of planar convex bodies of
arbitrary size and arbitrary intersections. In order to achieve a
-approximation, we reduce the traveling salesman problem with disks, up
to constant factors, to a minimum weight hitting set problem in a geometric
hypergraph. The connection between TSPN and hitting sets in geometric
hypergraphs, established here, is likely to have future applications.Comment: 14 pages, 3 figure
Hitting time for the continuous quantum walk
We define the hitting (or absorbing) time for the case of continuous quantum
walks by measuring the walk at random times, according to a Poisson process
with measurement rate . From this definition we derive an explicit
formula for the hitting time, and explore its dependence on the measurement
rate. As the measurement rate goes to either 0 or infinity the hitting time
diverges; the first divergence reflects the weakness of the measurement, while
the second limit results from the Quantum Zeno effect. Continuous-time quantum
walks, like discrete-time quantum walks but unlike classical random walks, can
have infinite hitting times. We present several conditions for existence of
infinite hitting times, and discuss the connection between infinite hitting
times and graph symmetry.Comment: 12 pages, 1figur
Almost uniform sampling via quantum walks
Many classical randomized algorithms (e.g., approximation algorithms for
#P-complete problems) utilize the following random walk algorithm for {\em
almost uniform sampling} from a state space of cardinality : run a
symmetric ergodic Markov chain on for long enough to obtain a random
state from within total variation distance of the uniform
distribution over . The running time of this algorithm, the so-called {\em
mixing time} of , is , where
is the spectral gap of .
We present a natural quantum version of this algorithm based on repeated
measurements of the {\em quantum walk} . We show that it
samples almost uniformly from with logarithmic dependence on
just as the classical walk does; previously, no such
quantum walk algorithm was known. We then outline a framework for analyzing its
running time and formulate two plausible conjectures which together would imply
that it runs in time when is
the standard transition matrix of a constant-degree graph. We prove each
conjecture for a subclass of Cayley graphs.Comment: 13 pages; v2 added NSF grant info; v3 incorporated feedbac
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