317 research outputs found
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
Reordering Buffer Management with a Logarithmic Guarantee in General Metric Spaces
In the reordering buffer management problem a sequence of requests arrive online in a finite metric space, and have to be processed by a single server. This server is equipped with a request buffer of size k and can decide at each point in time, which request from its buffer to serve next. Servicing of a request is simply done by moving the server to the location of the request. The goal is to process all requests while minimizing the total distance that the server is traveling inside the metric space.
In this paper we present a deterministic algorithm for the reordering buffer management problem that achieves a competitive ratio of O(log Delta + min {log n,log k}) in a finite metric space of n points and aspect ratio Delta. This is the first algorithm that works for general metric spaces and has just a logarithmic dependency on the relevant parameters. The guarantee is memory-robust, i.e., the competitive ratio decreases only slightly when the buffer-size of the optimum is increased to h=(1+epsilon)k. For memory robust guarantees our bounds are close to optimal
Polylogarithmic guarantees for generalized reordering buffer management
In the Generalized Reordering Buffer Management Problem (GRBM) a sequence of items located in a metric space arrives online, and has to be processed by a set of k servers moving within the space. In a single step the first b still unprocessed items from the sequence are accessible, and a scheduling strategy has to select an item and a server. Then the chosen item is processed by moving the chosen server to its location. The goal is to process all items while minimizing the total distance travelled by the servers. This problem was introduced in [Chan, Megow, Sitters, van Stee TCS 12] and has been subsequently studied in an online setting by [Azar, Englert, Gamzu, Kidron STACS 14]. The problem is a natural generalization of two very well-studied problems: the k-server problem for b=1 and the Reordering Buffer Management Problem (RBM) for k=1. In this paper we consider the GRBM problem on a uniform metric in the online version. We show how to obtain a competitive ratio of O(log k(log k+loglog b)) for this problem. Our result is a drastic improvement in the dependency on b compared to the previous best bound of O(√b log k), and is asymptotically optimal for constant k, because Ω(log k + loglog b) is a lower bound for GRBM on uniform metrics
Almost tight bounds for reordering buffer management
We give almost tight bounds for the online reordering buffer management problem on the uniform metric. Specifically, we present the first nontrivial lower bounds for this problem by showing that deterministic online algorithms have a competitive ratio of at least and randomized online algorithms have a competitive ratio of at least , where denotes the size of the buffer. We complement this by presenting a deterministic online algorithm for the reordering buffer management problem that obtains a competitive ratio of , almost matching the lower bound. This improves upon an algorithm by Avigdor-Elgrabli and Rabani that achieves a competitive ratio of
Randomization can be as helpful as a glimpse of the future in online computation
We provide simple but surprisingly useful direct product theorems for proving
lower bounds on online algorithms with a limited amount of advice about the
future. As a consequence, we are able to translate decades of research on
randomized online algorithms to the advice complexity model. Doing so improves
significantly on the previous best advice complexity lower bounds for many
online problems, or provides the first known lower bounds. For example, if
is the number of requests, we show that:
(1) A paging algorithm needs bits of advice to achieve a
competitive ratio better than , where is the cache
size. Previously, it was only known that bits of advice were
necessary to achieve a constant competitive ratio smaller than .
(2) Every -competitive vertex coloring algorithm must
use bits of advice. Previously, it was only known that
bits of advice were necessary to be optimal.
For certain online problems, including the MTS, -server, paging, list
update, and dynamic binary search tree problem, our results imply that
randomization and sublinear advice are equally powerful (if the underlying
metric space or node set is finite). This means that several long-standing open
questions regarding randomized online algorithms can be equivalently stated as
questions regarding online algorithms with sublinear advice. For example, we
show that there exists a deterministic -competitive -server
algorithm with advice complexity if and only if there exists a
randomized -competitive -server algorithm without advice.
Technically, our main direct product theorem is obtained by extending an
information theoretical lower bound technique due to Emek, Fraigniaud, Korman,
and Ros\'en [ICALP'09]
NP-hardness of the sorting buffer problem on the uniform metric
AbstractAn instance of the sorting buffer problem (SBP) consists of a sequence of requests for service, each of which is specified by a point in a metric space, and a sorting buffer which can store up to a limited number of requests and rearrange them. To serve a request, the server needs to visit the point where serving a request p following the service to a request q requires the cost corresponding to the distance d(p,q) between p and q. The objective of SBP is to serve all input requests in a way that minimizes the total distance traveled by the server by reordering the input sequence. In this paper, we focus our attention to the uniform metric, i.e., the distance d(p,q)=1 if p≠q, d(p,q)=0 otherwise, and present the first NP-hardness proof for SBP on the uniform metric
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