Dynamic Storage Allocation Problem Research Articles

From Spectrum Bonding to Contiguous-Resource Batching Task Scheduling

We formulate and analyze a generic task scheduling problem: a set of tasks need to be executed on a pool of continuous resource such as spectrum and memory, each requiring a certain amount of time and contiguous resource; some tasks can be executed simultaneously in batch by sharing the resource, while others requiring exclusive use of the resource. We seek an optimal resource allocation and the related scheduling policy maximizing the overall system utility. This problem, termed as the contiguous-resource batching task scheduling problem, arises in a variety of engineering fields, where communication and storage resources are potential bottlenecks and thus need to be carefully scheduled. Two motivating examples are the spectrum bonding problem in dynamic spectrum access systems and the dynamic storage allocation problem in computer systems. In this paper, we investigate both offline and online scheduling settings. We first establish the NP-hardness of the offline setting and the inapproximability of the online setting in its generic form. Given the theoretical performance limit, we then develop approximation algorithms with mathematically proven performance guarantee in terms of approximation and competitive ratios for the offline and online settings.

Single and multiple device DSA problems, complexities and online algorithms

We study the single-device Dynamic Storage Allocation (DSA) problem and the multi-device Balancing DSA problem in this paper. The goal is to dynamically allocate the job into memory to minimize the usage of space without concurrency. The SRF problem is just a variant of the DSA problem. Our results are as follows. • The NP-completeness for the 2-SRF problem, 3-DSA problem, and DSA problem for jobs with agreeable deadlines. • An improved 3-competitive algorithm for jobs with agreeable deadlines on single-device DSA problems. A 4-competitive algorithm for jobs with agreeable deadlines on multi-device Balancing DSA problems. • Lower bounds for jobs with agreeable deadlines: any non-clairvoyant algorithm cannot be ( 2 − ϵ ) -competitive and any clairvoyant algorithm cannot be ( 1.54 − ϵ ) -competitive. • The first O ( log L ) -competitive algorithm for general jobs on multi-device Balancing DSA problems without any assumption.

Max-coloring and online coloring with bandwidths on interval graphs

Given a graph G = ( V, E ) and positive integral vertex weights w : V → N , the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C 1 , C 2 , …, C k , minimize ∑ i =1 k max v ∈ C i w ( v ). This problem, restricted to interval graphs, arises whenever there is a need to design dedicated memory managers that provide better performance than the general-purpose memory management of the operating system. Though this problem seems similar to the dynamic storage allocation problem, there are fundamental differences. We make a connection between max-coloring and online graph coloring and use this to devise a simple 2-approximation algorithm for max-coloring on interval graphs. We also show that a simple first-fit strategy, that is a natural choice for this problem, yields an 8-approximation algorithm. We show this result by proving that the first-fit algorithm for online coloring an interval graph G uses no more than 8 ċ χ( G ) colors, significantly improving the bound of 26 ċ χ( G ) by Kierstead and Qin [1995]. We also show that the max-coloring problem is NP-hard. The problem of online coloring of intervals with bandwidths is a simultaneous generalization of online interval coloring and online bin packing. The input is a set I of intervals, each interval i ∈ I having an associated bandwidth b ( i ) ∈ (0, 1]. We seek an online algorithm that produces a coloring of the intervals such that for any color c and any real r , the sum of the bandwidths of intervals containing r and colored c is at most 1. Motivated by resource allocation problems, Adamy and Erlebach [2003] consider this problem and present an algorithm that uses at most 195 times the number of colors used by an optimal offline algorithm. Using the new analysis of first-fit coloring of interval graphs, we show that the Adamy-Erlebach algorithm is 35-competitive. Finally, we generalize the Adamy-Erlebach algorithm to a class of algorithms and show that a different instance from this class is 30-competitive.

Finite-size scaling approach to dynamic storage allocation problem

It is demonstrated how dynamic storage allocation algorithms can be analyzed in terms of finite-size scaling. The method is illustrated in the three simple cases of the first-fit, next-fit and best-fit algorithms, and the system works at full capacity. The analysis is done from two different points of view—running speed and employed memory. In both cases, and for all algorithms, it is shown that a simple scaling function exists and the relevant exponents are calculated. The method can be applied on similar problems as well.

An approximation result for a periodic allocation problem

In this paper we study a periodic allocation problem which is a generalization of the dynamic storage allocation problem to the case in which the arrival and departure time of each item is periodically repeated. These problems are equivalent to the interval coloring problem on weighted graphs in which each feasible solution corresponds to an acyclic orientation, and the solution value is equal to the length of the longest weighted path of the oriented graph. Optimal solutions correspond to acyclic orientations having the length of longest weighted path as small as possible. We prove that for the interval coloring problem on a class of circular arc graphs, and hence for a periodic allocation problem, there exists an approximation algorithm that finds a feasible solution whose value is at most two times the optimal.

A note on the dynamic storage allocation problem

A note on the dynamic storage allocation problem

A dynamic storage allocation problem

A dynamic storage allocation problem