Clock routing for high-performance ICs
DAC '90 Proceedings of the 27th ACM/IEEE Design Automation Conference
High-performance clock routing based on recursive geometric matching
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
DAC '92 Proceedings of the 29th ACM/IEEE Design Automation Conference
A clustering-based optimization algorithm in zero-skew routings
DAC '93 Proceedings of the 30th international Design Automation Conference
Bounded-skew clock and Steiner routing
ACM Transactions on Design Automation of Electronic Systems (TODAES)
A zero-skew clock routing scheme for VLSI circuits
ICCAD '92 Proceedings of the 1992 IEEE/ACM international conference on Computer-aided design
Minimizing wirelength in zero and bounded skew clock trees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Fast hierarchical clustering and other applications of dynamic closest pairs
Journal of Experimental Algorithmics (JEA)
Nearly linear time approximation schemes for Euclidean TSP and other geometric problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Multicast routing with end-to-end delay and delay variation constraints
IEEE Journal on Selected Areas in Communications
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The skew of an edge-weighted rooted tree is the maximum difference between any two root-to-leaf path weights. Zero- or bounded-skew trees are needed for achieving synchronization in many applications, including network multicasting [21] and VLSI clock routing [3, 18]. In these applications edge weights represent propagation delays, and a signal generated at the root should be received by multiple recipients located at the leaves (almost) simultaneously. The objective is to find zero- or bounded-skew trees of minimum total weight, since the weight of the tree is directly proportional to the amount of resources that must be allocated to the tree. Charikar et al. [9] have recently proposed the first strongly polynomial algorithms with proven constant approximation factors, 2e ≈ 5.44 and 16.86, for finding minimum weight zero- and bounded-skew trees, respectively.In this paper we introduce a new approach to these problems, based on zero-skew “stretching” of spanning trees, and obtain algorithms with improved approximation factors of 4 and 14. For the case when tree nodes are points in the plane and edge weights are given by the rectilinear metric our algorithms find zero- and bounded-skew trees of length at most 3 and 9 times the optimum. This case is of special interest in VLSI clock routing. An important feature of our algorithms is their practical running time, which is asymptotically the same as the time needed for computing the minimum spanning tree.