10 research outputs found
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
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
Determination of Project Management Technique using AHP Decision-Making in Projects
This study presents the Analytical Hierarchy Process (AHP) as a potential decision-making method of project management techniques in international trade project management. Forms created by AHP method with the involvement of 7 employees, including administrative and technical project managers and project planning supervisors working in the Project Management Organization of a leading engineering and technology company in Turkey, were collected by in-depth interview technique. After the consistency analysis, the final project management technique analysis was made. According to the findings obtained in the study, Result Orientation, Delivery Performance Competence and Installation Cost Efficiency were evaluated as the 3 most important criteria when deciding on the project management technique; that, the decision makers will apply in project management. It is possible to mention that AGILE project management is the most preferred technique. In future studies, the effect of creating an ideal project management technique framework in project management organizations can be examined based on the sequence of techniques revealed in this study and their superiorities
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
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 non-trivial lower bounds for this problem by showing that deterministic online algorithms have a competitive ratio of at least Ω(√{log k/log log k}) and randomized online algorithms have a competitive ratio of at least Ω(log log k), where k 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 O(√log k), almost matching the lower bound. This improves upon an algorithm by Avigdor-Elgrabli and Rabani (SODA 2010) that achieves a competitive ratio of O(log k/ log log k)
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]