Preemptive Scheduling of Equal-Length Jobs to Maximize Weighted Throughput

We study the problem of computing a preemptive schedule of equal-length jobs with given release times, deadlines and weights. Our goal is to maximize the weighted throughput, which is the total weight of completed jobs. In Graham's notation this problem is described as (1 | r_j;p_j=p;pmtn | sum w_j U_j). We provide an O(n^4)-time algorithm for this problem, improving the previous bound of O(n^{10}) by Baptiste.Comment: gained one author and lost one degree in the complexit

Throughput Maximization in the Speed-Scaling Setting

We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget of energy $E$ and we study the scheduling problem of maximizing the throughput (i.e. the number of jobs which are completed on time). We propose a dynamic programming algorithm that solves the preemptive case of the problem, i.e. when the execution of the jobs may be interrupted and resumed later, in pseudo-polynomial time. Our algorithm can be adapted for solving the weighted version of the problem where every job is associated with a weight $w_j$ and the objective is the maximization of the sum of the weights of the jobs that are completed on time. Moreover, we provide a strongly polynomial time algorithm to solve the non-preemptive unweighed case when the jobs have the same processing requirements. For the weighted case, our algorithm can be adapted for solving the non-preemptive version of the problem in pseudo-polynomial time.Comment: submitted to SODA 201

Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines

We study the classic weighted maximum throughput problem on unrelated machines. We give a (1-1/e-?)-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ?-approximation algorithm for the single-machine problem to obtain an approximation factor of (1-1/e)? -? for the corresponding unrelated-machines problem, for any ? > 0. On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1-1/e) -? for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine

How the structure of precedence constraints may change the complexity class of scheduling problems

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. We also show that there still are many very exciting challenges in this research area

Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems

The Preemptive Resource Allocation Problem

We revisit a classical scheduling model to incorporate modern trends in data center networks and cloud services. Addressing some key challenges in the allocation of shared resources to user requests (jobs) in such settings, we consider the following variants of the classic resource allocation problem (RAP). The input to our problems is a set J of jobs and a set M of homogeneous hosts, each has an available amount of some resource. A job is associated with a release time, a due date, a weight and a given length, as well as its resource requirement. A feasible schedule is an allocation of the resource to a subset of the jobs, satisfying the job release times/due dates as well as the resource constraints. A crucial distinction between classic RAP and our problems is that we allow preemption and migration of jobs, motivated by virtualization techniques. We consider two natural objectives: throughput maximization (MaxT), which seeks a maximum weight subset of the jobs that can be feasibly scheduled on the hosts in M, and resource minimization (MinR), that is finding the minimum number of (homogeneous) hosts needed to feasibly schedule all jobs. Both problems are known to be NP-hard. We first present an Omega(1)-approximation algorithm for MaxT instances where time-windows form a laminar family of intervals. We then extend the algorithm to handle instances with arbitrary time-windows, assuming there is sufficient slack for each job to be completed. For MinR we study a more general setting with d resources and derive an O(log d)-approximation for any fixed d >= 1, under the assumption that time-windows are not too small. This assumption can be removed leading to a slightly worse ratio of O(log d log^* T), where T is the maximum due date of any job

08071 Abstracts Collection -- Scheduling

From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available