This paper constructs a three-sector growth model with non-renewable environmental resource and a resource augmenting technological progress, and investigates the relation between the sustainability of resource use and growth of the nations. When the resource augmenting technological progress

We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal o-line algorithm is limited to m machines, for some xed m < n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n=m, the best on-line algorithm has a ratio which decays exponentially in n=m. Specically, we give a deterministic algorithm with competitive ratio of 1 + 2 n m (1 o(1)) , and a lower bound of 1 + e n m (1+o(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case. We show an on-line algorithm with a competitive ratio of 1 + e n m (1+o(1)) . We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m + 1, the greedy algorithm is optimal. (It is not optimal for permanent tasks.) A preliminary version of this paper appears in the proceedings of the 7th Biennial Scandinavian Workshop on Algorithm Theory, SWAT 2000. y Dept. of Computer Science, Tel-Aviv University. E-Mail: azar@math.tau.ac.il. Research supported in part by the Israel Science Foundation and by the United States-Israel Binational Science Foundation (BSF). z Dept. of Computer Science, Tel-Aviv University. E-Mail: lea@math.tau.ac.il. Part of the research was done while this author was visiting the Centre for Mathematics and Computer Science (CWI), supported by a grant from the Netherlands Organization of Scientic Research. x Centre for Mathematics and Computer Science (CWI). E-Mail: Rob.van.Stee@cwi.nl. Research supported by the Netherlands Organization for Scientic Research (NWO), project number SION 612-30-002. 1 1

, no good on-line algorithms exist for these problems, and for some variants no good off-line algorithms exist unless P = "P. We study these problems using a relaxed notion of competitive analysis, introduced by Kalyanasundaram and Pruhs, in which the on-line algorithm is allowed more resources than

It is known that online knapsack is not competitive. This negative result remains true even if the items are removable. In this paper we consider online removable knapsack with resource augmentation, in which we hold a knapsack of capacity R ≥ 1.0 and aim at maintaining a feasible packing

In competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b ≥ 2.

for a hard version of the problem where the sizes of the smallest and the largest jobs are not known in advance, only ∆ 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

results focus on how to achieve good performance when the same amount of resource is given to both the online and the optimal offline algorithms, i.e., one tree. In this paper, we focus on resource augmentation, where the online algorithm is allowed to use more trees than the optimal offline algorithm

resource augmentation, viz., processor speed-up, to guarantee desired real-time properties even under the presence of runtime overheads. We specifically consider preemptions and faults that, at runtime, manifest as overheads in the system in various ways. Our aim is to provide specified non

Many safety-critical embedded systems are sub-ject to certification requirements; some systems may be required to meet multiple sets of certification re-quirements, from different certification authorities. Certification requirements in such “mixed-criticality” systems give rise to some interesting scheduling prob-lems, that cannot be satisfactorily addressed using techniques from conventional scheduling theory. It had previously been shown that determining whether a sys-tem specified in this model can be scheduled to meet all its certification requirements is highly intractable. Prior work [4] had also introduced a simple, priority-based scheduling algorithm called OCBP for mixed criticality systems, and had quantified, via the metric of processor speedup factor, the effectiveness of OCBP in scheduling dual-criticality systems – systems sub-ject to two sets of certification requirements. In this paper, we extend this result to systems with arbitrarily many distinct criticality levels, by de-riving a quantitative processor speedup factor (that depends on n) for OCBP when scheduling systems with n criticality levels for arbitrary n. 1

ratios for flow time or stretch with arbitrarily small resource augmentation. Both the randomized and the deterministic load balancing algorithms are nonmigratory and do immediate dispatch of jobs. The randomized