A survey on buffered clock tree synthesis for skew. In each merging step, three sets of possible locations for embedding an internal node of the abstract topology are computed. If the skew of ts is zero then t s is a zeroskew tree zst. In what follows, we address the zero skew clock routing problem. An example of a tree of merging segments with sinks s1s8. The problem is to construct a clock tree with zero skew to achieve synchronicity and minimal sum of edge lengths so that circuit area and clock tree capacitance are minimized. In this section, we present our temperature aware clocktree optimization algorithm, taco, which incrementally optimizes a given zero skew clock tree constructed under the uniform thermal condition. Clock skew sometimes called timing skew is a phenomenon in synchronous digital circuit systems such as computer systems in which the same sourced clock signal arrives at different components at different times. We propose a clusteringbased algorithm which uses shortest. Experimental results show that the pathlength skew of our routing tree. However, the algorithm will require n time to detect this. A tree is a nonlinear data structure, compared to arrays, linked lists, stacks and queues which are linear data structures.
The htree algorithm can be implemented using the steps as shown in figure 1. A clusteringbased optimization algorithm in zeroskew. An algorithm for zeroskew clock tree routing with buffer. A clock tree router for general skew constraints cecs. An algorithm for zeroskew clock tree routing with buffer insertion. The operation of most digital circuits is synchronized by a periodic. Advanced vlsi design agrawal 1 zeroskew clock routing ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ff ck. An exact zeroskew clock routing algorithm computer. Our boundedskew routing algorithm, called the bstdme algorithm, extends the dme algorithm for exact zeroskew trees via the concept of a merging region. Then, based on the idea of typematching clock tree, we propose a zero skew gated clock tree synthesis algorithm. In this pap er, w e prop ose a zeroskew routing algorithm that is muc h simpler and practically more e cien t than the clusteringbased algorithm. Nanoscale vlsi clock routing module based on usefulskew.
The dynamic nearestneighbor algorithm dnna to generate tree topology and the walksegment breadth first. Our algorithm only needs o1 space at each node, overall on 17 implementations in real implementations, some more issues. Compared with the industrystrength gated clock tree synthesis, experimental data show that our approach can significantly reduce the clock skew in every process corner with a small penalty on the clock tree area and the clock tree. Integer is if haschildren node then result sk ew clo c k tree with resp ect to the. With this new insight, we designed an effective onlogntime o1approximation algorithm and an optimal dynamic programming for zst construction. The deferredmerge embedding dme algorithm was introduced for zeroskew clocktree routing independently by edahiro 9, 11, chao et al. The clock routing trees produced by our method attain almost zero skew with only modest wirelength penalty. Symmetrical buffer placement in clock trees for minimal skew immune to global onchip variations renshen wang 1. It will still have an eigenvaluezero eigenvector supported on the root if and only if the formula evaluates to zero. Minimizing wirelength in zero and bounded skew clock trees. A stretched tree t is a zeroskew tree zst if all roottoleaf paths in t have. In this scenario our algorithm produces a clock routing tree that is embedded in the channel intersection graph 10 of an arbitrary buildingblock layout.
Additionally, wirelength of clock routing trees should be. Moreover, zeroskew and boundedskew sched ules may not always be legitimate. In linear time, it embeds any given connection topology into the manhattan plane to create a clock tree with zero skew while minimizing total wire length. Were upgrading the acm dl, and would like your input. The routing algorithm used in this tool is based on the exact zero skew routing algorithm. A single layer zero skew clock routing in x architecture. A tree can be empty with no nodes or a tree is a structure consisting of one node called the root and zero or one or more subtrees.
An exact zero skew clock routing algorithm using elmore delay model is presented. Zero or boundedskew trees are needed for achieving synchronization in many applications, including network multicasting g. Clock tree synthesis for timing convergence and timing. The greedybstdme algorithm very closely matches the best known heuristics for the zeroskew case and for the unboundedskew case i. A clocksynthesis methodology for spiceaccurate skew optimization with tolerance to voltage variations was proposed in 14.
Although the clokc skew in equidistant routings is usually eryv small 3, equidistant routings are not exact zero skew in general. A tree is called a perfect pathlength balanced tree if its pathlength skew is zero. Skewed trees relation to binary search tree stack overflow. The optimized clock trees are zeroskew, or free from designinherited clock skews, and their processinduced clock skews are reduced by clock delay minimization. Equivalence between zeroskew tree zst and hierarchical clustering hc on points p p1,p2,p3,p4. The algorithm can be applied to singlestaged clock trees, multistaged clock trees, and multichip system clock trees. Despite the possibility of increasing the skew variation by inserting a crosslink, the authors in 12 propose an effective algorithm that. Recursively in a bottomup fashion, two zeroskewed subtrees are merged into a. I am trying to understand implementation of linear time suffix array creation algorithm by karkkainen, p. An exact zeroskew clock routing algorithm computeraided design of in tegrated circuits and systems, ieee transactions on author. In summary, our k ey con tributions in this pap er are. We give the first constantfactor approximation algorithms for this problem and its. It searched for a good, easytorealize clock layout, called the use ful skew tree ust, under general clock skew constraints.
The skew of ts is the maximum value of its0, s, ts0, s,l over all sink pairs s3 e s. Danaher professor ece department, auburn university auburn, al 36849 email protected spring 2014, mar 17. This algorithm is foundational to all the latest developments in clock. A stretched tree consisting of an arborescence, a mapping such that is a onetoone mapping between the leaves of and and a cost function such that for every edge of, and furthermore, for. Power efficient treebased crosslinks for skew reduction.
Understanding implementation of dc3skew algorithm to. For a prescribed topology, bstdme constructs a boundedskew tree bst in two phases. A rc network model was applied to these algorithms, so that exact zero skew routings were nally achieved 16. The methodology has been tested using a real design database and resulting in a significant improvement in the through put time required to complete the clock tree generation. Wong 1996, an algorithm for zeroskew clock tree routing with buffer insertion, in european design and test conference, ieee proceedings. An exact zeroskew clock routing algorithm ieee xplore. Another good definition is a binary tree of n nodes such that its depth is n1.
Fast clock tree generation using exact zero skew clock. Typematching clock tree for zero skew clock gating. Given a set s of sink locations, construct a zst ts with minimum cost. Dmebased zeroskew algorithms can be adapted to handle the. When m is the l 1 plane, we refer to the l 1 variants of these problems. The pathlength skew of a tree is defined to be the maximum difference of the pathlengths in tbe tree from the root to any two leaves. A good definition for a skew tree is a binary tree such that all the nodes except one have one and only one child. Recursively in a bottomup fashion, two zeroskewed subtrees are merged into a new tree with zero skew. Mathematically, an unordered tree or algebraic tree can be. Construction algorithm an overview sciencedirect topics.
The buffered clock tree construction algorithm in vittal 1995 is an extension of the greedydme algorithm to consider the insertion of intermediate clock buffers during the construction of a zeroskew routing tree. Usefulskew tree ust algorithm based on deferredmerge embedding dme. Pdf practical approximation algorithms for zero and. With its advantages in wirelength reduction and routing flexibility compared with conventional manhattan routing, x architecture has been proposed and applied to modern ic design. Finally, 22 further enhance the bst algorithm and proposed an incremental scheduling technique to compute the feasibleskew range for constructing a usefulskew tree ust for general skew constraints. Though it is easy to produce zero skew clock routing trees see e. We proposed a lineartime optimal tree decomposition algorithm. Their proposed htree algorithm is based on the construction of. Symmetrical buffer placement in clock trees for minimal. We study the problem of multistage zero skew clock tree construction for minimizing clock phase delay and wirelength.
Abstract the skew of an edgeweighted rooted tree is the maximum difference between any two roottoleaf path weights. Clock tree synthesis based on wire length minimization. Practical approximation algorithms for zero and boundedskew. The exact zero skew clock routing algorithm, proposed by tsay in 1993 is still used in many clock tree synthesis tools. For a given topology, it outputs the locations of steiner points achieving zero skew and optimal wirelength. Pdf an exact zero skew clock routing algorithm using the elmore delay model is. The corresponding graph is nearly the lengthnline graph. The algorithm always yields exact zero skew trees with respect to the appropriate. Among them, deferredmerge embedding zstdme is a dynamic programming approach 6. The time complexity of our algorithm is linear on the a v erage. Clocktree routing realizing a clockschedule for semi. This algorithm was improedv to calculate exact equidistant routings 3,4 11.
Basically, taco migrates the tree nodes to new locations to reduce the worst case clock skew under thermal variation. The remainder of the pap er is organized as follo ws. Quality of service multicast zero skew tree problem. The skew of an edgeweighted rooted tree is the maximum difference between any two roottoleaf path weights. Zeroskew clock routing trees with minimum wirelength kenneth d. Elec 7770 advanced vlsi design spring 2014 zeroskew clock routing vishwani d. The ustbp algorithm of 17 was the first work that incorpo rated a flavor of simultaneous clock scheduling and routing. An exact zero skew clock routing algorithm using the elmore delay model is presented. The instantaneous difference between the readings of any two clocks is called their skew. As a critical part in highperformance integrated circuits, clock network design meets great challenges due to feature size decrease and clock frequency increase.
A zeroskew clock tree optimization algorithmfor clock delay and power optimization is proposed. Several algorithms have been proposed which all achieve zero clock skew at the cost of varying complexity, wire lengths, and other measures. The simplest approach was first proposed by dhar, franklin, and wang 2. In existing approaches clock buffers are inserted only after clock tree is constructed. Algorithmic tuning of clock trees and derived nontree. Tree height general case an on algorithm, n is the number of nodes in the tree require node. Minimum wirelength zero skew clock routing trees with. Practical approximation algorithms for zero and boundedskew trees alexander z. Details of algorithm can be found here i managed to understand overall concept but failing to match it with provided implementation and hence not. Practical approximation algorithms for zero and bounded.
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