Rejecting Jobs to Minimize Load and Maximum Flow-time

Online algorithms are usually analyzed using the notion of competitive ratio which compares the solution obtained by the algorithm to that obtained by an online adversary for the worst possible input sequence. Often this measure turns out to be too pessimistic, and one popular approach especially for scheduling problems has been that of "resource augmentation" which was first proposed by Kalyanasundaram and Pruhs. Although resource augmentation has been very successful in dealing with a variety of objective functions, there are problems for which even a (arbitrary) constant speedup cannot lead to a constant competitive algorithm. In this paper we propose a "rejection model" which requires no resource augmentation but which permits the online algorithm to not serve an epsilon-fraction of the requests. The problems considered in this paper are in the restricted assignment setting where each job can be assigned only to a subset of machines. For the load balancing problem where the objective is to minimize the maximum load on any machine, we give O(\log^2 1/\eps)-competitive algorithm which rejects at most an \eps-fraction of the jobs. For the problem of minimizing the maximum weighted flow-time, we give an O(1/\eps^4)-competitive algorithm which can reject at most an \eps-fraction of the jobs by weight. We also extend this result to a more general setting where the weights of a job for measuring its weighted flow-time and its contribution towards total allowed rejection weight are different. This is useful, for instance, when we consider the objective of minimizing the maximum stretch. We obtain an O(1/\eps^6)-competitive algorithm in this case. Our algorithms are immediate dispatch, though they may not be immediate reject. All these problems have very strong lower bounds in the speed augmentation model

Restricted Adaptivity in Stochastic Scheduling

We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee ?((log m)/(log log m)). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of ?-delay and ?-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an ?(log log m)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any ?-delay and ?-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy

Competitive Kill-and-Restart and Preemptive Strategies for Non-Clairvoyant Scheduling

We study kill-and-restart and preemptive strategies for the fundamental scheduling problem of minimizing the sum of weighted completion times on a single machine in the non-clairvoyant setting. First, we show a lower bound of~$3$ for any deterministic non-clairvoyant kill-and-restart strategy. Then, we give for any $b > 1$ a tight analysis for the natural $b$-scaling kill-and-restart strategy as well as for a randomized variant of it. In particular, we show a competitive ratio of $(1+3\sqrt{3})\approx 6.197$ for the deterministic and of $\approx 3.032$ for the randomized strategy, by making use of the largest eigenvalue of a Toeplitz matrix. In addition, we show that the preemptive Weighted Shortest Elapsed Time First (WSETF) rule is $2$-competitive when jobs are released online, matching the lower bound for the unit weight case with trivial release dates for any non-clairvoyant algorithm. Using this result as well as the competitiveness of round-robin for multiple machines, we prove performance guarantees smaller than $10$ for adaptions of the $b$-scaling strategy to online release dates and unweighted jobs on identical parallel machines.Comment: An extended abstract occurred in the Proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimizatio

Algorithms for Scheduling Problems and Integer Programming

The first part of this thesis gives approximation results to scheduling problems. The classical makespan minimization problem on identical parallel machines asks for a distribution of a set of jobs to a set of machines such that the latest job completion time is minimized. For this strongly NP-complete problem we give a new EPTAS algorithm. In fact, it admits a practical implementation which beats the currently best approximation ratio of the MULTIFIT algorithm. A well-studied extension of the problem is the partition of the jobs into classes which impose a class-specific setup time on a machine whenever the processing switches to a job of a different class. For these so-called scheduling problems with batch setup times we present a 1.5-approximation algorithm for each of the three major settings. We achieve similar results for the likewise natural variant of many shared resources scheduling (MSRS) where instead of imposing a setup time each class is identified by a resource which can be occupied by at most one of its jobs at a time. For MSRS we present a 1.5-approximation and two EPTAS results. The second part provides results for fixed-priority uniprocessor real-time scheduling and variants of block-structured integer programming. We give a new approach to compute worst-case response times which admits a polynomial-time algorithm for harmonic periods even in the presence of task release jitters. In more detail, we prove a duality between Response Time Computation (RTC) and the Mixing Set problem. Furthermore, both problems can be expressed as block-structured integer programs which are closely related to simultaneous congruences. However, the setting of the famous Chinese Remainder Theorem is that each congruence has to have a certain remainder. We relax this setting such that the remainder of each congruence may lie in a given interval. We show that the smallest solution to these congruences can be computed in polynomial time if the set of divisors is harmonic

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

Fundamentals

Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum