Alexander V. Kononov

Longer growing seasons do not increase net carbon uptake in the northeastern Siberian tundra

With global warming, snowmelt is occurring earlier and growing seasons are becoming longer around the Arctic. It has been suggested that this would lead to more uptake of carbon due to a lengthening of the period in which plants photosynthesize. To investigate this suggestion, 8 consecutive years of eddy covariance measurements at a northeastern Siberian graminoid tundra site were investigated for patterns in net ecosystem exchange, gross primary production (GPP) and ecosystem respiration (R-eco). While GPP showed no clear increase with longer growing seasons, it was significantly increased in warmer summers. Due to these warmer temperatures however, the increase in uptake was mostly offset by an increase in R-eco. Therefore, overall variability in net carbon uptake was low, and no relationship with growing season length was found. Furthermore, the highest net uptake of carbon occurred with the shortest and the coldest growing season. Low uptake of carbon mostly occurred with longer or warmer growing seasons. We thus conclude that the net carbon uptake of this ecosystem is more likely to decrease rather than to increase under a warmer climate. These results contradict previous research that has showed more net carbon uptake with longer growing seasons. We hypothesize that this difference is due to site-specific differences, such as climate type and soil, and that changes in the carbon cycle with longer growing seasons will not be uniform around the Arctic. (Less)

Complexity and approximability of scheduling resumable proportionally deteriorating jobs

A set of independent, resumable and proportionally deteriorating jobs is to be executed on a single machine. The machine is not continuously available for processing but the number of non-availability periods, the start time and end time of each period are known in advance. The criterion of schedule optimality is the maximum completion time. It is proved that the decision version of the problem with a single non-availability period is ordinarily -complete. It is also proved that for the problem with a single non-availability period there exists a fully polynomial-time approximation scheme. Finally, it is proved that for the problem with two or more non-availability periods there does not exist a polynomial-time approximation algorithm with a constant worst-case ratio, unless .

On the approximate tradeoff for bicriteria batching and parallel machine scheduling problems

We consider multiobjective scheduling problems, i.e. scheduling problems that are evaluated with respect to many cost criteria, and we are interested in determining a trade-off (Pareto curve) among these criteria. We study two types of bicriteria scheduling problems: single-machine batching problems and parallel machine scheduling problems. Instead of proceeding in a problem-by-problem basis, we identify a class of multiobjective optimization problems possessing a fully polynomial time approximation scheme (FPTAS) for computing an ?-approximate Pareto curve. This class contains a set of problems whose Pareto curve can be computed via a simple pseudo-polynomial dynamic program for which the objective and transition functions satisfy some, easy to verify, arithmetical conditions. Our study is based on a recent work of Woeginger (Electronic Colloquium on Computational Complexity, Report 84 (short version appeared in SODA?99, pp. 820?829)) for the single criteria optimization ex-benevolent problems. We show how our general result can be applied to the considered scheduling problems.

A FPTAS for Approximating the Unrelated Parallel Machines Scheduling Problem with Costs

We consider the classical problem of scheduling a set of independent jobs on a set of unrelated machines with costs. We are given a set of n monoprocessor jobs and m machines where each job is to be processed without preemptions. Executing job j on machine i requires time pij ≥ 0 and incurs cost cij . Our objective is to find a schedule obtaining a tradeoff between the makespan and the total cost. We focus on the case where the number of machines is a fixed constant, and we propose a simple FPTAS that computes for any Ɛ > 0 a schedule with makespan at most (1+Ɛ)T and cost at most Copt(T), in time O(n(n/Ɛ)m), given that there exists a schedule of makespan T, where Copt(T) is the cost of the minimum cost schedule which achieves a makespan of T. We show that the optimal makespan-cost trade-off (Pareto) curve can be approximated by an efficient polynomial time algorithm within any desired accuracy. Our results can also be applied to the scheduling problem where the rejection of jobs is allowed. Each job has a penalty associated to it, and one is allowed to schedule any subset of jobs. In this case the goal is the minimization of the makespan of the scheduled jobs and the total penalty of the rejected jobs.

Customer order scheduling to minimize the number of late jobs

In the order scheduling problem, every job (order) consists of several tasks (product items), each of which will be processed on a dedicated machine. The completion time of a job is defined as the time at which all its tasks are finished. Minimizing the number of late jobs was known to be strongly NP-hard. In this note, we show that no FPTAS exists for the two-machine, common due date case, unless P = NP. We design a heuristic algorithm and analyze its performance ratio for the unweighted case. An LP-based approximation algorithm is presented for the general multicover problem. The algorithm can be applied to the weighted version of the order scheduling problem with a common due date.

Approximation algorithms for scheduling problems with exact delays

We give first constant-factor approximations for various cases of the coupled-task single machine and two-machine flow shop scheduling problems with exact delays and makespan as the objective function. In particular, we design 3.5- and 3-approximation algorithms for the general cases of the single-machine and the two-machine problems, respectively. We also prove that the existence of a (2−e)-approximation algorithm for the single-machine problem as well as the existence of a (1.5−e)-approximation algorithm for the two-machine problem implies P=NP. The inapproximability results are valid for the cases when the operations of each job have equal processing times and for these cases the approximation ratios achieved by our algorithms are very close to best possible: we prove that the single machine problem is approximable within a factor of 2.5 and the two-machine problem is approximable within a factor of 2.

Isomorphic scheduling problems

We consider general properties of isomorphic scheduling problems that constitute a new class of pairs of mutually related scheduling problems. Any such a pair is composed of a scheduling problem with fixed job processing times and its time-dependent counterpart with processing times that are proportional-linear functions of the job starting times. In order to introduce the class formally, first we formulate a generic scheduling problem with fixed job processing times and define isomorphic problems by a one-to-one transformation of instances of the generic problem into instances of time-dependent scheduling problems with proportional-linear job processing times. Next, we prove basic properties of isomorphic scheduling problems and show how to convert polynomial algorithms for scheduling problems with fixed job processing times into polynomial algorithms for proportional-linear counterparts of the original problems. Finally, we show how are related approximation algorithms for isomorphic problems. Applying the results, we establish new worst-case results for time-dependent parallel-machine scheduling problems and prove that many single- and dedicated-machine time-dependent scheduling problems with proportional-linear job processing times are polynomially solvable.

Energy Efficient Scheduling and Routing via Randomized Rounding

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed scalable processors in a fully heterogeneous setting. For both the preemptive-nonmigratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-nonmigratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.

From Preemptive to Non-preemptive Speed-Scaling Scheduling

We are given a set of jobs, each one specified by its release date, its deadline and its processing volume (work), and a single (or a set of) speed-scalable processor(s). We adopt the standard model in speed-scaling in which if a processor runs at speed s then the energy consumption is s α units of energy per time unit, where α > 1. Our goal is to find a schedule respecting the release dates and the deadlines of the jobs so that the total energy consumption is minimized. While most previous works have studied the preemptive case of the problem, where a job may be interrupted and resumed later, we focus on the non-preemptive case where once a job starts its execution, it has to continue until its completion without any interruption. As the preemptive case is known to be polynomially solvable for both the single-processor and the multiprocessor case, we explore the idea of transforming an optimal preemptive schedule to a non-preemptive one. We prove that the preemptive optimal solution does not preserve enough of the structure of the non-preemptive optimal solution, and more precisely that the ratio between the energy consumption of an optimal non-preemptive schedule and the energy consumption of an optimal preemptive schedule can be very large even for the single-processor case. Then, we focus on some interesting families of instances: (i) equal-work jobs on a single-processor, and (ii) agreeable instances in the multiprocessor case. In both cases, we propose constant factor approximation algorithms. In the latter case, our algorithm improves the best known algorithm of the literature. Finally, we propose a (non-constant factor) approximation algorithm for general instances in the multiprocessor case.

Properties of optimal schedules in preemptive shop scheduling

In this work we show that certain classical preemptive shop scheduling problems with integral data satisfy the following integer preemption property: there exists an optimal preemptive schedule where all interruptions and all starting and completion times occur at integral dates. We also give new upper bounds on the minimal number of interruptions for various shop scheduling problems.