Handling False Loops in Processing Unit Design

Processing unit design is an important step in the design of video signal processors. The main problem is to find a mapping of a set of Signal Flow Graphs (SFGs), specifying part of the functional behavior of an Integrated Circuit, onto Processing Units (PUs), describing the hardware and its interconnection. The pursued approach to PU design consists of four consecutive steps: allocation of operators, assignment of operations to operators, operator splitting, and retiming. Central in PU design is the minimization of chip area. Resource sharing provides a means to achieve this. It is a technique which makes it possible to map several SFGs onto a single MFPU. A precondition is that only one of the SFGs is executed at the same time. The current decomposition strategy of multiplexing possibly introduces false loops in the resulting MFPU, which makes retiming at PU level and timing verification impossible. In the thesis we address the problem of false loops. We give a mathematic..

Scheduling on identical machines: How good is LPT in an on-line setting?

. We consider a parallel machine scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on m identical machines, where preemption is not allowed and the number of jobs is unknown in advance. Each job becomes available at its release date, which is not known in advance, and its processing time becomes known at its arrival. We deal with the problem of minimizing the makespan, which is the time by which all jobs have been finished. We propose and analyze the following on-line lpt algorithm: At any time a machine becomes available for processing, schedule an available job with the largest processing time. We prove that this algorithm has a performance guarantee of 3=2. Furthermore, we show that any on-line algorithm will have a performance bound of at least 1.3473. This bound is improved to (5 \Gamma p 5)=2 ß 1:3820 for m = 2. 1 Introduction Until a few years ago, one of the basic assumptions in deterministic scheduling was that all of the informat..

On-line Scheduling of Two-Machine Open Shops where Jobs Arrive Over Time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan. Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while in the nonclairvoyant on-line model, this processing requirement is not known until the job is processed and completed. In both models, scheduling of a job is irrevocable. We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5=4 (preemptive) and 3=2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3=2 (preemptive and non-preemptive). Keywords. scheduling, open shop, makespan, o..

On-line scheduling of two-machine open shops where jobs arrive over time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan. Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while in the non-clairvoyant on-line model, this processing requirement is not known until the job is processed and completed. In both models, scheduling of a job is irrevocable. We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5/4 (preemptive) and 3/2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3/2 (preemptive and non-preemptive)

Masterplan toekomst wiskunde

Dit masterplan is na uitgebreide consultatie opgesteld namens de academische wiskundige gemeenschap van Nederland. De Nederlandse wiskunde heeft dankzij de recente clustering van het onderzoek, de toenemende nationale samenwerking in het wetenschappelijk onderwijs en de door het ministerie van OCW aangekondigde hervormingen van het voortgezet onderwijs per 2013, een vernieuwende dynamiek ontwikkeld. Met dit plan stellen wij een aantal acties voor om deze veranderingen in het wiskundige landschap te verankeren en de resterende problemen aan te pakken. Tevens gaat speciale aandacht uit naar de valorisatie van wiskunde in Nederland

Scheduling on identical machines: How good is

. We consider a parallel machine scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on m identical machines, where preemption is not allowed and the number of jobs is unknown in advance. Each job becomes available at its release date, which is not known in advance, and its processing time becomes known at its arrival. We deal with the problem of minimizing the makespan, which is the time by which all jobs have been finished. We propose and analyze the following on-line lpt algorithm: At any time a machine becomes available for processing, schedule an available job with the largest processing time. We prove that this algorithm has a performance guarantee of 3=2. Furthermore, we show that any on-line algorithm will have a performance bound of at least 1.3473. This bound is improved to (5 \Gamma p 5)=2 1:3820 for m = 2. 1 Introduction Until a few years ago, one of the basic assumptions in deterministic scheduling was that all of the informat..

Lower Bounds for on-Line Single-Machine Scheduling

The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total flow time. By using new techniques, we provide the first lower bounds for several of these problems, and we significantly improve the bounds that were known