V.Th. Paschos

Time slot scheduling of compatible jobs

A version of weighted coloring of a graph is introduced which is motivated by some types of scheduling problems: each node v of a graph G corresponds to some operation to be processed (with a processing time w(v)), edges represent nonsimultaneity requirements (incompatibilities). We have to assign each operation to one time slot in such a way that in each time slot, all operations assigned to this slot are compatible; the length of a time slot will be the maximum of the processing times of its operations. The number k of time slots to be used has to be determined as well. So, we have to find a k-coloring

Bridging gap between standard and differential polynomial approximation: the case of bin-packing

{\cal S}

An O*(1.0977 n ) exact algorithm for MAX INDEPENDENT SET in sparse graphs

=

Probabilistic coloring of bipartite and split graphs

({S_{1},\ldots ,S_{k}})

A hypocoloring model for batch scheduling

of G such that w(S1) + ⋅s +w(Sk) is minimized where w(Si) = max {w(v) :v∊V}. Properties of optimal solutions are discussed, and complexity and approximability results are presented. Heuristic methods are given for establishing some of these results. The associated decision problems are shown to be NP-complete for bipartite graphs, for line-graphs of bipartite graphs, and for split graphs.

Reductions, completeness and the hardness of approximability

We study the approximation of min set cover combining ideas and results from polynomial approximation and from exact computation (with non-trivial worst case complexity upper bounds) for NP-hard problems. We design approximation algorithms for min set cover achieving ratios that cannot be achieved in polynomial time (unless problems in NP could be solved by slightly super-polynomial algorithms) with worst-case complexity much lower (though super-polynomial) than those of an exact computation.