4 research outputs found
A Bicriteria Approximation for the Reordering Buffer Problem
In the reordering buffer problem (RBP), a server is asked to process a
sequence of requests lying in a metric space. To process a request the server
must move to the corresponding point in the metric. The requests can be
processed slightly out of order; in particular, the server has a buffer of
capacity k which can store up to k requests as it reads in the sequence. The
goal is to reorder the requests in such a manner that the buffer constraint is
satisfied and the total travel cost of the server is minimized. The RBP arises
in many applications that require scheduling with a limited buffer capacity,
such as scheduling a disk arm in storage systems, switching colors in paint
shops of a car manufacturing plant, and rendering 3D images in computer
graphics.
We study the offline version of RBP and develop bicriteria approximations.
When the underlying metric is a tree, we obtain a solution of cost no more than
9OPT using a buffer of capacity 4k + 1 where OPT is the cost of an optimal
solution with buffer capacity k. Constant factor approximations were known
previously only for the uniform metric (Avigdor-Elgrabli et al., 2012). Via
randomized tree embeddings, this implies an O(log n) approximation to cost and
O(1) approximation to buffer size for general metrics. Previously the best
known algorithm for arbitrary metrics by Englert et al. (2007) provided an
O(log^2 k log n) approximation without violating the buffer constraint.Comment: 13 page
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
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