4,287 research outputs found
The reverse greedy algorithm for the metric k-median problem
The Reverse Greedy algorithm (RGreedy) for the k-median problem works as
follows. It starts by placing facilities on all nodes. At each step, it removes
a facility to minimize the resulting total distance from the customers to the
remaining facilities. It stops when k facilities remain. We prove that, if the
distance function is metric, then the approximation ratio of RGreedy is between
?(log n/ log log n) and O(log n).Comment: to appear in IPL. preliminary version in COCOON '0
Coordination of Mobile Mules via Facility Location Strategies
In this paper, we study the problem of wireless sensor network (WSN)
maintenance using mobile entities called mules. The mules are deployed in the
area of the WSN in such a way that would minimize the time it takes them to
reach a failed sensor and fix it. The mules must constantly optimize their
collective deployment to account for occupied mules. The objective is to define
the optimal deployment and task allocation strategy for the mules, so that the
sensors' downtime and the mules' traveling distance are minimized. Our
solutions are inspired by research in the field of computational geometry and
the design of our algorithms is based on state of the art approximation
algorithms for the classical problem of facility location. Our empirical
results demonstrate how cooperation enhances the team's performance, and
indicate that a combination of k-Median based deployment with closest-available
task allocation provides the best results in terms of minimizing the sensors'
downtime but is inefficient in terms of the mules' travel distance. A
k-Centroid based deployment produces good results in both criteria.Comment: 12 pages, 6 figures, conferenc
A Constant Approximation for Colorful k-Center
In this paper, we consider the colorful k-center problem, which is a generalization of the well-known k-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius rho, such that with k balls of radius rho, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a "pseudo-approximation" algorithm that works in any metric space, and an approximation algorithm that works for a special class of instances in the plane. The latter algorithm uses a novel connection to a certain matching problem in graphs
Incremental Medians via Online Bidding
In the k-median problem we are given sets of facilities and customers, and
distances between them. For a given set F of facilities, the cost of serving a
customer u is the minimum distance between u and a facility in F. The goal is
to find a set F of k facilities that minimizes the sum, over all customers, of
their service costs.
Following Mettu and Plaxton, we study the incremental medians problem, where
k is not known in advance, and the algorithm produces a nested sequence of
facility sets where the kth set has size k. The algorithm is c-cost-competitive
if the cost of each set is at most c times the cost of the optimum set of size
k. We give improved incremental algorithms for the metric version: an
8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive
randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic
algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized
algorithm.
The algorithm is s-size-competitive if the cost of the kth set is at most the
minimum cost of any set of size k, and has size at most s k. The optimal
size-competitive ratios for this problem are 4 (deterministic) and e
(randomized). We present the first poly-time O(log m)-size-approximation
algorithm for the offline problem and first poly-time O(log m)-size-competitive
algorithm for the incremental problem.
Our proofs reduce incremental medians to the following online bidding
problem: faced with an unknown threshold T, an algorithm submits "bids" until
it submits a bid that is at least the threshold. It pays the sum of all its
bids. We prove that folklore algorithms for online bidding are optimally
competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via
Online Bidding
Lagrangian Relaxation and Partial Cover
Lagrangian relaxation has been used extensively in the design of
approximation algorithms. This paper studies its strengths and limitations when
applied to Partial Cover.Comment: 20 pages, extended abstract appeared in STACS 200
An Experimental Investigation of Hyperbolic Routing with a Smart Forwarding Plane in NDN
Routing in NDN networks must scale in terms of forwarding table size and
routing protocol overhead. Hyperbolic routing (HR) presents a potential
solution to address the routing scalability problem, because it does not use
traditional forwarding tables or exchange routing updates upon changes in
network topologies. Although HR has the drawbacks of producing sub-optimal
routes or local minima for some destinations, these issues can be mitigated by
NDN's intelligent data forwarding plane. However, HR's viability still depends
on both the quality of the routes HR provides and the overhead incurred at the
forwarding plane due to HR's sub-optimal behavior. We designed a new forwarding
strategy called Adaptive Smoothed RTT-based Forwarding (ASF) to mitigate HR's
sub-optimal path selection. This paper describes our experimental investigation
into the packet delivery delay and overhead under HR as compared with
Named-Data Link State Routing (NLSR), which calculates shortest paths. We run
emulation experiments using various topologies with different failure
scenarios, probing intervals, and maximum number of next hops for a name
prefix. Our results show that HR's delay stretch has a median close to 1 and a
95th-percentile around or below 2, which does not grow with the network size.
HR's message overhead in dynamic topologies is nearly independent of the
network size, while NLSR's overhead grows polynomially at least. These results
suggest that HR offers a more scalable routing solution with little impact on
the optimality of routing paths
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