153,714 research outputs found
The Online Disjoint Set Cover Problem and its Applications
Given a universe of elements and a collection of subsets
of , the maximum disjoint set cover problem (DSCP) is to
partition into as many set covers as possible, where a set cover
is defined as a collection of subsets whose union is . We consider the
online DSCP, in which the subsets arrive one by one (possibly in an order
chosen by an adversary), and must be irrevocably assigned to some partition on
arrival with the objective of minimizing the competitive ratio. The competitive
ratio of an online DSCP algorithm is defined as the maximum ratio of the
number of disjoint set covers obtained by the optimal offline algorithm to the
number of disjoint set covers obtained by across all inputs. We propose an
online algorithm for solving the DSCP with competitive ratio . We then
show a lower bound of on the competitive ratio for any
online DSCP algorithm. The online disjoint set cover problem has wide ranging
applications in practice, including the online crowd-sourcing problem, the
online coverage lifetime maximization problem in wireless sensor networks, and
in online resource allocation problems.Comment: To appear in IEEE INFOCOM 201
Ramsey-type theorems for metric spaces with applications to online problems
A nearly logarithmic lower bound on the randomized competitive ratio for the
metrical task systems problem is presented. This implies a similar lower bound
for the extensively studied k-server problem. The proof is based on Ramsey-type
theorems for metric spaces, that state that every metric space contains a large
subspace which is approximately a hierarchically well-separated tree (and in
particular an ultrametric). These Ramsey-type theorems may be of independent
interest.Comment: Fix an error in the metadata. 31 pages, 0 figures. Preliminary
version in FOCS '01. To be published in J. Comput. System Sc
On the Continuous CNN Problem
In the (discrete) CNN problem, online requests appear as points in
. Each request must be served before the next one is revealed. We
have a server that can serve a request simply by aligning either its or
coordinate with the request. The goal of the online algorithm is to minimize
the total distance traveled by the server to serve all the requests. The
best known competitive ratio for the discrete version is 879 (due to Sitters
and Stougie).
We study the continuous version, in which, the request can move continuously
in and the server must continuously serve the request. A simple
adversarial argument shows that the lower bound on the competitive ratio of any
online algorithm for the continuous CNN problem is 3. Our main contribution is
an online algorithm with competitive ratio . Our
analysis is tight. The continuous version generalizes the discrete orthogonal
CNN problem, in which every request must be or aligned with the
previous request. Therefore, Our result improves upon the previous best
competitive ratio of 9 (due to Iwama and Yonezawa)
A -Competitive Algorithm for Scheduling Packets with Deadlines
In the online packet scheduling problem with deadlines (PacketScheduling, for
short), the goal is to schedule transmissions of packets that arrive over time
in a network switch and need to be sent across a link. Each packet has a
deadline, representing its urgency, and a non-negative weight, that represents
its priority. Only one packet can be transmitted in any time slot, so, if the
system is overloaded, some packets will inevitably miss their deadlines and be
dropped. In this scenario, the natural objective is to compute a transmission
schedule that maximizes the total weight of packets which are successfully
transmitted. The problem is inherently online, with the scheduling decisions
made without the knowledge of future packet arrivals. The central problem
concerning PacketScheduling, that has been a subject of intensive study since
2001, is to determine the optimal competitive ratio of online algorithms,
namely the worst-case ratio between the optimum total weight of a schedule
(computed by an offline algorithm) and the weight of a schedule computed by a
(deterministic) online algorithm.
We solve this open problem by presenting a -competitive online
algorithm for PacketScheduling (where is the golden ratio),
matching the previously established lower bound.Comment: Major revision of the analysis and some other parts of the paper.
Another revision will follo
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