Jhm Jan Korst

Periodic multiprocessor scheduling

A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods.

Improved force-directed scheduling in high-throughput digital signal processing

This paper discusses improved force-directed scheduling and its application in the design of high-throughput DSP systems, such as real-time video VLSL circuits. We present a mathematical justification of the technique of force-directed scheduling, introduced by Paulin and Knight (1989), and we show how the algorithm can be used to find cost-effective time assignments and resource allocations, allowing trade-offs between processing units and memories. Furthermore, we present modifications that improve the effectiveness and the efficiency of the algorithm. The significance of the improvements is illustrated by an empirical performance analysis based on a number of problem instances. >

Improved force-directed scheduling

Presents a mathematical justification of the technique of force-directed scheduling and propose two modifications of the basic algorithm introduced by Paulin and Knight. The newly presented modifications improve the effectiveness of force-directed scheduling without affecting its time complexity. This is illustrated by an empirical performance analysis based on a number of problem instances.<<ETX>>

Periodic assignment and graph colouring

We analyse the problem of executing periodic operations on a minimum number of identical processors under different constraints. The analysis is based on a reformulation of the problem in terms of graph colouring. It is shown that different constraints result in colouring problems defined on different classes of graphs, viz. interval graphs, circular-arc graphs and periodic-interval graphs. We discuss the complexity of these colouring problems in detail.

A variable-depth search algorithm for the recursive bipartitioning of signal flow graphs

We discuss the use of local search techniques for mapping video algorithms onto programmable high-performance video signal processors. The mapping problem is very complex due to many constraints that need to be satisfied in order to obtain a feasible solution. The complexity is reduced by decomposing the mapping problem into three subproblems, namely delay management, partitioning, and scheduling. We present the partitioning problem and the representation of video algorithms by signal flow graphs. Furthermore, we propose a solution strategy that is based on recursive bipartitioning of these graphs. The bipartitions are generated using a variable-depth search algorithm. The results demonstrate that the frequently cited flexibility of local search techniques can be successfully exploited in handling complicated problems.ZusammenfassungVideoalgorithmen transformieren Videosignale, also die zur Bilderzeugung notwendigen Informationseinheiten, um Bildqualität oder die Möglichkeiten spezieller Features, wie Teletext oder Bild-in-Bild-Wiedergabe, zu erhöhen. Eigene, anwendungsspezifische und häufig nur einem Videoalgorithmus zuteilbare, schnelle Videosignalprozessoren sind für die Ausführung von Videoalgorithmen verantwortlich. Die Zuordnung der Algorithmen und Prozessoren ist, aufgrund der großen Zahl zu beachtender Restriktionen, ein NP-schweres Problem, so daß eine Aufspaltung in die drei Teilprobleme Terminierung, Partitionierung und Scheduling von Operationen sinnvoll wird. In der vorliegenden Arbeit werden das Partitionierungsproblem und die Beschreibung von Videoalgorithmen mittels Signalflußgraphen betrachtet. Ein auf lokaler Suche basierendes Lösungsverfahren erzeugt rekursiv Bipartitionen des Graphen, die komplexe Nachbarschaften variabler Tiefe generieren. Rechenergebnisse zeigen, daß die vielzitierte Universalität und Flexibilität lokaler Suchverfahren erfolgreich zur Lösung schwieriger, stark restringierter Probleme genutzt werden können.

Smoothing Streams in an In-Home Digital Network: Optimization of Bus and Buffer Usage

In an in-home digital network it may be expected that several data streams (audio, video) run simultaneously over a shared communication device, e.g., a bus. The burstiness of a data stream can be reduced by buffering data at the sending and receiving side, thereby allowing a lower bus share allocation for the stream. In this paper we present an algorithm that determines how much of the bus capacity and buffer space should be allocated to each stream, in order to have a feasible transmission schedule for each stream. Furthermore, the algorithm determines a transmission schedule for each stream, indicating how much data is transmitted over time. We show how this multiple-stream problem can be solved by repeatedly solving single-stream problems. We present efficient algorithms to solve these single-stream problems. Furthermore, we present some experimental results.

The complexity of generalized retiming problems

We discuss the complexity of a number of high-level synthesis problems that can be viewed as generalizations of the classical retiming problem introduced by Leiserson and Saxe. The generalizations are concerned with additional degrees of freedom resulting from timefolding and multiplexing. The central problem is the design of multicycle and multifunctional processing units. This problem consists of two subproblems known as operator assignment and retiming. In this paper, we are primarily concerned with the construction of appropriate models and their complexity analysis. We show that both operator assignment and retiming are NP-hard in the presence of multiplexing or timefolding. We present a novel proof of the result obtained by Leiserson and Saxe, which states that retiming without multiplexing or timefolding can be solved in polynomial time.

Random redundant storage in disk arrays: complexity of retrieval problems

Random redundant data storage strategies have proven to be a good choice for efficient data storage in multimedia servers. These strategies lead to a retrieval problem in which it is decided for each requested data block which disk to use for its retrieval. In this paper, we give a complexity classification of retrieval problems for random redundant storage.

Periodic scheduling in a multimedia server

We describe how the problem of effectively servicing a number of users by a multimedia server can be represented as a periodic disk scheduling problem. We give an overview of related work and present a number of new results, based on periodically servicing users that have different consumption requirements with different periods. In addition, by scheduling sets of disk accesses as batches the worst-case switching overhead is reduced.

Computer-assisted proof of performance ratios for the Differencing Method☆

Abstract We consider the problem of partitioning a set of n numbers into m subsets of cardinality k = ⌈ n / m ⌉ or ⌊ n / m ⌋ , such that the maximum subset sum is minimal. We show that the performance ratio of the Differencing Method of Karmarkar and Karp for solving this problem is at least 2 − ∑ i = 0 k − 1 i ! k ! for any fixed k . We also build a mixed integer linear programming model ( milp ) whose solution yields the performance ratio for any given k . For k ≤ 7 these milp -instances can be solved with an exact milp -solver. This results in a computer-assisted proof of the tightness of the aforementioned lower bound for k ≤ 7 . For k > 7 we prove that 2 − 1 k − 1 is an upper bound on the performance ratio, thereby leaving a gap with the lower bound of Θ ( k − 3 ) , which is less than 0.4%.