Notes on Max Flow Time Minimization with Controllable Processing Times

In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the identical parallel machines max flow time minimization problem with controllable processing times. We address the preemptive and non-preemptive version of the problem. For the preemptive case, a linear programming formulation is presented which solves the problem optimally in polynomial time. For the non-preemptive problem it is shown that the First In First Out (FIFO) heuristic has a tight worst-case performance of 3−2/m, when jobs processing times and costs are set as in some optimal preemptive schedul

Optimal on-line flow time with resource augmentation

AbstractWe study the problem of scheduling n jobs that arrive over time. We consider a non-preemptive setting on a single machine. The goal is to minimize the total flow time. We use extra resource competitive analysis: an optimal off-line algorithm which schedules jobs on a single machine is compared to a more powerful on-line algorithm that has ℓ machines. We design an algorithm of competitive ratio 1+2min(Δ1/ℓ,n1/ℓ), where Δ is the maximum ratio between two job sizes, and provide a lower bound which shows that the algorithm is optimal up to a constant factor for any constant ℓ. The algorithm works for a hard version of the problem where the sizes of the smallest and the largest jobs are not known in advance, only Δ and n are known. This gives a trade-off between the resource augmentation and the competitive ratio.We also consider scheduling on parallel identical machines. In this case the optimal off-line algorithm has m machines and the on-line algorithm has ℓm machines. We give a lower bound for this case. Next, we give lower bounds for algorithms using resource augmentation on the speed. Finally, we consider scheduling with hard deadlines, and scheduling so as to minimize the total completion time

Minimización del tiempo total de flujo de tareas en una sola máquina: Estado del arte

La programación de operaciones en una sola máquina es un problema clásico de la investigación de operaciones. Numerosos métodos han sido propuestos para resolver diferentes instancias del problema, dependiendo de las restricciones impuestas y del objetivo del mismo. En este artículo estamos interesados en ilustrar el estado actual de desarrollo de los métodos y algoritmos existentes en la literatura para el problema de minimización del flujo total de tareas sujetas a fechas de llegadas, tanto en problemas estáticos como dinámicos. Además, las posibilidades de trabajo y las preguntas abiertas serán igualmente expuestas

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions

Independent Set, Induced Matching, and Pricing: Connections and Tight (Subexponential Time) Approximation Hardnesses

We present a series of almost settled inapproximability results for three fundamental problems. The first in our series is the subexponential-time inapproximability of the maximum independent set problem, a question studied in the area of parameterized complexity. The second is the hardness of approximating the maximum induced matching problem on bounded-degree bipartite graphs. The last in our series is the tight hardness of approximating the k-hypergraph pricing problem, a fundamental problem arising from the area of algorithmic game theory. In particular, assuming the Exponential Time Hypothesis, our two main results are: - For any r larger than some constant, any r-approximation algorithm for the maximum independent set problem must run in at least 2^{n^{1-\epsilon}/r^{1+\epsilon}} time. This nearly matches the upper bound of 2^{n/r} (Cygan et al., 2008). It also improves some hardness results in the domain of parameterized complexity (e.g., Escoffier et al., 2012 and Chitnis et al., 2013) - For any k larger than some constant, there is no polynomial time min (k^{1-\epsilon}, n^{1/2-\epsilon})-approximation algorithm for the k-hypergraph pricing problem, where n is the number of vertices in an input graph. This almost matches the upper bound of min (O(k), \tilde O(\sqrt{n})) (by Balcan and Blum, 2007 and an algorithm in this paper). We note an interesting fact that, in contrast to n^{1/2-\epsilon} hardness for polynomial-time algorithms, the k-hypergraph pricing problem admits n^{\delta} approximation for any \delta >0 in quasi-polynomial time. This puts this problem in a rare approximability class in which approximability thresholds can be improved significantly by allowing algorithms to run in quasi-polynomial time.Comment: The full version of FOCS 201

Existence Theorems for Scheduling to Meet Two Objectives

We will look at the existence of schedules which are simultaneously near-optimal for two criteria. First,we will present some techniques for proving existence theorems,in a very general setting,for bicriterion scheduling problems. We will then use these techniques to prove existence theorems for a large class of problems. We will consider the relationship between objective functions based on completion time,flow time,lateness and the number of on-time jobs. We will also present negative results first for the problem of simultaneously minimizing the maximum flow time and average weighted flow time and second for minimizing the maximum flow time and simultaneously maximizing the number of on-time jobs. In some cases we will also present lower bounds and algorithms that approach our bicriterion existence theorems. Finally we will improve upon our general existence results in one more specific environment

Interactive proof system variants and approximation algorithms for optical networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (p. 111-121).by Ravi Sundaram.Ph.D