42,551 research outputs found
Super-Fast Distributed Algorithms for Metric Facility Location
This paper presents a distributed O(1)-approximation algorithm, with
expected- running time, in the model for
the metric facility location problem on a size- clique network. Though
metric facility location has been considered by a number of researchers in
low-diameter settings, this is the first sub-logarithmic-round algorithm for
the problem that yields an O(1)-approximation in the setting of non-uniform
facility opening costs. In order to obtain this result, our paper makes three
main technical contributions. First, we show a new lower bound for metric
facility location, extending the lower bound of B\u{a}doiu et al. (ICALP 2005)
that applies only to the special case of uniform facility opening costs. Next,
we demonstrate a reduction of the distributed metric facility location problem
to the problem of computing an O(1)-ruling set of an appropriate spanning
subgraph. Finally, we present a sub-logarithmic-round (in expectation)
algorithm for computing a 2-ruling set in a spanning subgraph of a clique. Our
algorithm accomplishes this by using a combination of randomized and
deterministic sparsification.Comment: 15 pages, 2 figures. This is the full version of a paper that
appeared in ICALP 201
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
Pseudo-Separation for Assessment of Structural Vulnerability of a Network
Based upon the idea that network functionality is impaired if two nodes in a
network are sufficiently separated in terms of a given metric, we introduce two
combinatorial \emph{pseudocut} problems generalizing the classical min-cut and
multi-cut problems. We expect the pseudocut problems will find broad relevance
to the study of network reliability. We comprehensively analyze the
computational complexity of the pseudocut problems and provide three
approximation algorithms for these problems.
Motivated by applications in communication networks with strict
Quality-of-Service (QoS) requirements, we demonstrate the utility of the
pseudocut problems by proposing a targeted vulnerability assessment for the
structure of communication networks using QoS metrics; we perform experimental
evaluations of our proposed approximation algorithms in this context
Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees
In a directed graph with non-correlated edge lengths and costs, the
\emph{network design problem with bounded distances} asks for a cost-minimal
spanning subgraph subject to a length bound for all node pairs. We give a
bi-criteria -approximation for this
problem. This improves on the currently best known linear approximation bound,
at the cost of violating the distance bound by a factor of at
most~.
In the course of proving this result, the related problem of \emph{directed
shallow-light Steiner trees} arises as a subproblem. In the context of directed
graphs, approximations to this problem have been elusive. We present the first
non-trivial result by proposing a
-ap\-proxi\-ma\-tion, where are the
terminals.
Finally, we show how to apply our results to obtain an
-approximation for
\emph{light-weight directed -spanners}. For this, no non-trivial
approximation algorithm has been known before. All running times depends on
and and are polynomial in for any fixed
A Super-Fast Distributed Algorithm for Bipartite Metric Facility Location
The \textit{facility location} problem consists of a set of
\textit{facilities} , a set of \textit{clients} , an
\textit{opening cost} associated with each facility , and a
\textit{connection cost} between each facility and client
. The goal is to find a subset of facilities to \textit{open}, and to
connect each client to an open facility, so as to minimize the total facility
opening costs plus connection costs. This paper presents the first
expected-sub-logarithmic-round distributed O(1)-approximation algorithm in the
model for the \textit{metric} facility location problem on
the complete bipartite network with parts and . Our
algorithm has an expected running time of rounds, where . This result can be viewed as a continuation
of our recent work (ICALP 2012) in which we presented the first
sub-logarithmic-round distributed O(1)-approximation algorithm for metric
facility location on a \textit{clique} network. The bipartite setting presents
several new challenges not present in the problem on a clique network. We
present two new techniques to overcome these challenges. (i) In order to deal
with the problem of not being able to choose appropriate probabilities (due to
lack of adequate knowledge), we design an algorithm that performs a random walk
over a probability space and analyze the progress our algorithm makes as the
random walk proceeds. (ii) In order to deal with a problem of quickly
disseminating a collection of messages, possibly containing many duplicates,
over the bipartite network, we design a probabilistic hashing scheme that
delivers all of the messages in expected- rounds.Comment: 22 pages. This is the full version of a paper that appeared in DISC
201
Dynamic vs Oblivious Routing in Network Design
Consider the robust network design problem of finding a minimum cost network
with enough capacity to route all traffic demand matrices in a given polytope.
We investigate the impact of different routing models in this robust setting:
in particular, we compare \emph{oblivious} routing, where the routing between
each terminal pair must be fixed in advance, to \emph{dynamic} routing, where
routings may depend arbitrarily on the current demand. Our main result is a
construction that shows that the optimal cost of such a network based on
oblivious routing (fractional or integral) may be a factor of
\BigOmega(\log{n}) more than the cost required when using dynamic routing.
This is true even in the important special case of the asymmetric hose model.
This answers a question in \cite{chekurisurvey07}, and is tight up to constant
factors. Our proof technique builds on a connection between expander graphs and
robust design for single-sink traffic patterns \cite{ChekuriHardness07}
Self-Organizing Flows in Social Networks
Social networks offer users new means of accessing information, essentially
relying on "social filtering", i.e. propagation and filtering of information by
social contacts. The sheer amount of data flowing in these networks, combined
with the limited budget of attention of each user, makes it difficult to ensure
that social filtering brings relevant content to the interested users. Our
motivation in this paper is to measure to what extent self-organization of the
social network results in efficient social filtering. To this end we introduce
flow games, a simple abstraction that models network formation under selfish
user dynamics, featuring user-specific interests and budget of attention. In
the context of homogeneous user interests, we show that selfish dynamics
converge to a stable network structure (namely a pure Nash equilibrium) with
close-to-optimal information dissemination. We show in contrast, for the more
realistic case of heterogeneous interests, that convergence, if it occurs, may
lead to information dissemination that can be arbitrarily inefficient, as
captured by an unbounded "price of anarchy". Nevertheless the situation differs
when users' interests exhibit a particular structure, captured by a metric
space with low doubling dimension. In that case, natural autonomous dynamics
converge to a stable configuration. Moreover, users obtain all the information
of interest to them in the corresponding dissemination, provided their budget
of attention is logarithmic in the size of their interest set
Designing Networks with Good Equilibria under Uncertainty
We consider the problem of designing network cost-sharing protocols with good
equilibria under uncertainty. The underlying game is a multicast game in a
rooted undirected graph with nonnegative edge costs. A set of k terminal
vertices or players need to establish connectivity with the root. The social
optimum is the Minimum Steiner Tree. We are interested in situations where the
designer has incomplete information about the input. We propose two different
models, the adversarial and the stochastic. In both models, the designer has
prior knowledge of the underlying metric but the requested subset of the
players is not known and is activated either in an adversarial manner
(adversarial model) or is drawn from a known probability distribution
(stochastic model).
In the adversarial model, the designer's goal is to choose a single,
universal protocol that has low Price of Anarchy (PoA) for all possible
requested subsets of players. The main question we address is: to what extent
can prior knowledge of the underlying metric help in the design? We first
demonstrate that there exist graphs (outerplanar) where knowledge of the
underlying metric can dramatically improve the performance of good network
design. Then, in our main technical result, we show that there exist graph
metrics, for which knowing the underlying metric does not help and any
universal protocol has PoA of , which is tight. We attack this
problem by developing new techniques that employ powerful tools from extremal
combinatorics, and more specifically Ramsey Theory in high dimensional
hypercubes.
Then we switch to the stochastic model, where each player is independently
activated. We show that there exists a randomized ordered protocol that
achieves constant PoA. By using standard derandomization techniques, we produce
a deterministic ordered protocol with constant PoA.Comment: This version has additional results about stochastic inpu
- …