When the greedy algorithm fails

When the greedy algorithm fails

We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in an independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection problem. The practical message of this paper is that the greedy algorithm should be used with great car...

When the Decreasing Sequence Fails

The classical method for program analysis by abstract interpretation consists in computing a increasing sequence with widening, which converges towards a correct solution, then computing a decreasing sequence of correct solutions without widening. It is generally admitted that, when the decreasing sequence reaches a fixpoint, it cannot be improved further. As a consequence, all efforts for impr...

When Bellman's Principle Fails

We present several examples which show that the well known statements about Markov Decision Processes can fail if the loss function is not bounded.

When Sharing Fails

When Abstraction Fails

Reasoning about programs is mostly deduction: the reasoning from the abstract model to the concrete run. Deduction is useful because it allows us to predict properties of future runs—up to the point that a program will never fail its specification. However, even such a 100% correct program may still show a problem: the specification itself may be problematic, or deduction required us to abstrac...