446 research outputs found
Randomized online computation with high probability guarantees
We study the relationship between the competitive ratio and the tail
distribution of randomized online minimization problems. To this end, we define
a broad class of online problems that includes some of the well-studied
problems like paging, k-server and metrical task systems on finite metrics, and
show that for these problems it is possible to obtain, given an algorithm with
constant expected competitive ratio, another algorithm that achieves the same
solution quality up to an arbitrarily small constant error a with high
probability; the "high probability" statement is in terms of the optimal cost.
Furthermore, we show that our assumptions are tight in the sense that removing
any of them allows for a counterexample to the theorem. In addition, there are
examples of other problems not covered by our definition, where similar high
probability results can be obtained.Comment: 20 pages, 2 figure
Dynamic Balanced Graph Partitioning
This paper initiates the study of the classic balanced graph partitioning
problem from an online perspective: Given an arbitrary sequence of pairwise
communication requests between nodes, with patterns that may change over
time, the objective is to service these requests efficiently by partitioning
the nodes into clusters, each of size , such that frequently
communicating nodes are located in the same cluster. The partitioning can be
updated dynamically by migrating nodes between clusters. The goal is to devise
online algorithms which jointly minimize the amount of inter-cluster
communication and migration cost.
The problem features interesting connections to other well-known online
problems. For example, scenarios with generalize online paging, and
scenarios with constitute a novel online variant of maximum matching. We
present several lower bounds and algorithms for settings both with and without
cluster-size augmentation. In particular, we prove that any deterministic
online algorithm has a competitive ratio of at least , even with significant
augmentation. Our main algorithmic contributions are an -competitive deterministic algorithm for the general setting with
constant augmentation, and a constant competitive algorithm for the maximum
matching variant
Online Service with Delay
In this paper, we introduce the online service with delay problem. In this
problem, there are points in a metric space that issue service requests
over time, and a server that serves these requests. The goal is to minimize the
sum of distance traveled by the server and the total delay in serving the
requests. This problem models the fundamental tradeoff between batching
requests to improve locality and reducing delay to improve response time, that
has many applications in operations management, operating systems, logistics,
supply chain management, and scheduling.
Our main result is to show a poly-logarithmic competitive ratio for the
online service with delay problem. This result is obtained by an algorithm that
we call the preemptive service algorithm. The salient feature of this algorithm
is a process called preemptive service, which uses a novel combination of
(recursive) time forwarding and spatial exploration on a metric space. We hope
this technique will be useful for related problems such as reordering buffer
management, online TSP, vehicle routing, etc. We also generalize our results to
servers.Comment: 30 pages, 11 figures, Appeared in 49th ACM Symposium on Theory of
Computing (STOC), 201
Paging and Registration in Cellular Networks: Jointly Optimal Policies and an Iterative Algorithm
This paper explores optimization of paging and registration policies in
cellular networks. Motion is modeled as a discrete-time Markov process, and
minimization of the discounted, infinite-horizon average cost is addressed. The
structure of jointly optimal paging and registration policies is investigated
through the use of dynamic programming for partially observed Markov processes.
It is shown that there exist policies with a certain simple form that are
jointly optimal, though the dynamic programming approach does not directly
provide an efficient method to find the policies.
An iterative algorithm for policies with the simple form is proposed and
investigated. The algorithm alternates between paging policy optimization and
registration policy optimization. It finds a pair of individually optimal
policies, but an example is given showing that the policies need not be jointly
optimal. Majorization theory and Riesz's rearrangement inequality are used to
show that jointly optimal paging and registration policies are given for
symmetric or Gaussian random walk models by the nearest-location-first paging
policy and distance threshold registration policies.Comment: 13 pages, submitted to IEEE Trans. Information Theor
Polynomial-Time Approximation Scheme for Data Broadcast
The data broadcast problem is to find a schedule for broadcasting a given set
of messages over multiple channels. The goal is to minimize the cost of the
broadcast plus the expected response time to clients who periodically and
probabilistically tune in to wait for particular messages.
The problem models disseminating data to clients in asymmetric communication
environments, where there is a much larger capacity from the information source
to the clients than in the reverse direction. Examples include satellites,
cable TV, internet broadcast, and mobile phones. Such environments favor the
``push-based'' model where the server broadcasts (pushes) its information on
the communication medium and multiple clients simultaneously retrieve the
specific information of individual interest.
This paper presents the first polynomial-time approximation scheme (PTAS) for
data broadcast with O(1) channels and when each message has arbitrary
probability, unit length and bounded cost. The best previous polynomial-time
approximation algorithm for this case has a performance ratio of 9/8
Optimal Eviction Policies for Stochastic Address Traces
The eviction problem for memory hierarchies is studied for the Hidden Markov
Reference Model (HMRM) of the memory trace, showing how miss minimization can
be naturally formulated in the optimal control setting. In addition to the
traditional version assuming a buffer of fixed capacity, a relaxed version is
also considered, in which buffer occupancy can vary and its average is
constrained. Resorting to multiobjective optimization, viewing occupancy as a
cost rather than as a constraint, the optimal eviction policy is obtained by
composing solutions for the individual addressable items.
This approach is then specialized to the Least Recently Used Stack Model
(LRUSM), a type of HMRM often considered for traces, which includes V-1
parameters, where V is the size of the virtual space. A gain optimal policy for
any target average occupancy is obtained which (i) is computable in time O(V)
from the model parameters, (ii) is optimal also for the fixed capacity case,
and (iii) is characterized in terms of priorities, with the name of Least
Profit Rate (LPR) policy. An O(log C) upper bound (being C the buffer capacity)
is derived for the ratio between the expected miss rate of LPR and that of OPT,
the optimal off-line policy; the upper bound is tightened to O(1), under
reasonable constraints on the LRUSM parameters. Using the stack-distance
framework, an algorithm is developed to compute the number of misses incurred
by LPR on a given input trace, simultaneously for all buffer capacities, in
time O(log V) per access.
Finally, some results are provided for miss minimization over a finite
horizon and over an infinite horizon under bias optimality, a criterion more
stringent than gain optimality.Comment: 37 pages, 3 figure
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