The problem of Scheduling $n$ Independent Jobs on $m$ Unrelated Parallel Machines, when $m$ is fixed, is considered. The standard problem of minimizing the makespan of the schedule (SUM) and the bicriteria problem of scheduling with bounded makespan and cost (SUMC), are addressed, and randomized fully linear time approximation schemes ... more >>>

We consider the problem of finding a $k$-vertex ($k$-edge) connected spanning subgraph $K$ of a given $n$-vertex graph $G$ while minimizing the maximum degree $d$ in $K$. We give a polynomial time algorithm for fixed $k$ that achieves an $O(\log n)$-approximation. The only known previous polynomial algorithms achieved degree $d+1$ ... more >>>