In a system in which noncooperative agents share a common resource, we propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the eeectiveness of the system. Deriving upper and lower bounds for this ratio in a model in which several agents share a very simple network leads to some interesting mathematics, results, and open problems.

Hard real-time systems are subject to timing constraints and failure to respectthem can cause economic, ecological or human disasters. The validation processwhich guarantees the safety of such software, by ensuring the respect of theseconstraints in all situations including the worst case, is based on the knowledgeof the worst case execution time of each task. However, determini...

Dynamic memory management is an important aspect of modern software engineering techniques. However, developers of real-time systems avoid using it because they fear that the worst-case execution time of the dynamic memory allocation routines is not bounded or is bounded with an excessively large bound. The degree to which this concern is valid is quantified in this paper, by giving detailed av...

The original Leapfrogging Samplesort operates on a sorted sample of size s and an unsorted part of size s+1. We generalize this to a sorted sample of size s and an unsorted part of size (2 − 1)(s+1), where k = O(1). We present a practical implementation of this class of algorithms and we show that the worst-case complexity is O(n log n) and the average-case complexity is O(n log n).

So far we have dealt mostly with the worst-case complexity of problems. We might also wonder aobut the average-case complexity of a problem, namely, how difficult the problem is to solve for an instance chosen randomly from some distribution. It may be the case for a certain problem that hard instances exist but are extremely rare. Many reductions use very specifically constructed problems, so ...

We improve a connection of the worst-case complexity and the average-case complexity of some well-known lattice problems. This fascinating connection was rst discovered by Ajtai 1] in 1996. We improve the exponent of this connection from 8 to 3:5 + .