Scheduling Series-Parallel Orders Subject to 0/1-Communication Delays

We consider the problem P}&;| prec},cij&;{0,1}|κ of scheduling jobs with arbitrary processing times on sufficiently many parallel processors subject to series-parallel precedence constraints and 0/1-communication delays in order to minimize a regular performance measure κ. Such schedules without processor restrictions are used for generating approximate solutions for a restricted number of processors

Switchbox Routing in VLSI Design: Closing the Complexity Gap

The design of integrated circuits has achieved a great deal of attention in the last decade. In the routing phase, there have survived two open layout problems which are important from both the theoretical and the practical point of view. Up to now, switchbox routing has been known to be solvable in polynomial time when there are only 2-terminal nets, and to be NP}-complete in case there exist nets involving at least five terminals. Our main result is that this problem is NP}-complete even if no net has more that three terminals. Hence, from the theoretical perspective, the SRP is completely settled. The NP–completeness proof is based on a reduction from a special kind of the satisfiability problem. It is also possible to adopt our construction to channel routing which shows that this problem is NP–complete, even if each net does not consist of more than five terminals. This improves upon a result of Sarrafzadeh who proved the NP–completeness in case of nets with no more than six terminals

A Simple Approximation Algorithm for Scheduling Forests with Unit Processing Times and Zero-One Communication Delays

In the last few years, scheduling jobs due to communication delays has received a great deal of attention. We consider the problem of scheduling forests due to unit processing times and zero-one communication delays and focus on the approximation algorithm of Hanen and Munier and on the algorithm of Guinand, Rapine and Trystram. These algorithms and their analysis are quite complex. In contrast, we present a very simple list scheduling algorithm for the problem Pjprec=tree; p j = 1; c i j 2 f0;1gjC max of scheduling trees subject to unit processing times and zero-one communication delays. For sufficiently many machines, e.g. m jV j, the resulting schedule is optimal. For a restricted number of machines, the presented algorithm has the same absolute worst case performance as the algorithm of Guinand, Rapine and Trystram: m\Gamma1 2 . It's relative worst case performance ratio turns out to be bounded by \Gamma 2 \Gamma 1 m \Delta even for arbitrary processing times. This simpli..