On a new timing-driven routing tree problem [FPGA]

In this paper, we consider a new model of timing-driven routing, based on the idea of finding minimum spanning trees (minimum routing cost) with bounded delays, in a multiple weighted graph. This problem is originally motivated by the timing-driven routing for FPGA´s, and is applicable to other related problems in which multiple independent optimization objectives need to be considered simultaneously. We prove that this problem in general is NP-complete, and there exists no approximation algorithm with any constant bound for the problem if the triangle inequality does not hold. We give approximation algorithms with a guaranteed performance bound for the case when the routing cost satisfies the triangle inequality. Experimental results show that our algorithms are very promising