Alak Kumar Datta

Algorithms for high performance two-layer channel routing

Crosstalk minimization is one of the most important high performance aspects in interconnecting VLSI circuits. With advancement of fabrication technology, devices and interconnecting wires are placed in closer proximity and circuits operate at higher frequencies. This results in crosstalk between wire segments. Crosstalk minimization problem for the reserved two-layer Manhattan channel routing is NP-hard, even if the channel instances are free from any vertical constraint (simplest channel instances). In this paper we have developed heuristic algorithms for computing reduced crosstalk two-layer channel routing solutions for simplest as well as general channel instances. In general, the results obtained are highly encouraging.

A graph based algorithm to minimize total wire length in VLSI channel routing

Minimization of total (vertical) wire length is one of the most important problems in laying out blocks in VLSI physical design. Minimization of wire length not only reduces the cost of physical wiring required, but also reduces the electrical hazards of having long wires in the interconnection, power consumption, and signal propagation delays. Since the problem of computing minimum wire length routing solutions in no-dogleg, two-layer channel routing is NP-hard, it is interesting to develop heuristic algorithms that compute routing solutions of as low total (vertical) wire length as possible. In this paper we develop an efficient heuristic algorithm for appreciably reducing the total wire length in the reserved two-layer no-dogleg Manhattan channel routing model. Experimental results obtained are greatly encouraging.

Hardness of crosstalk minimization in two-layer channel routing

Crosstalk minimization is one of the most important aspects of high-performance VLSI circuit design. With the advancement of fabrication technology, devices and interconnecting wires are being placed in close vicinity, and circuits are operating at higher frequencies. This results in crosstalk between adjacent wire segments. In this paper, it has been shown that the crosstalk minimization problem in the reserved two-layer Manhattan routing model is NP-complete, even if channels are free from all vertical constraints. It has also been demonstrated that it is hard to approximate the crosstalk minimization problem. Besides, the issue of minimizing bottleneck crosstalk has been introduced that is a new problem for crosstalk minimization. It has been proven that this problem is also NP-complete. It has been further shown that all these results hold even if doglegging is allowed. Crosstalk minimisation is one of the most important aspects of high-performance VLSI circuit design.Crosstalk minimisation in the reserved two-layer Manhattan routing model is NP-complete, even without vertical constraints.It is hard to approximate the crosstalk minimisation problem.The problem of minimising bottleneck crosstalk is also NP-complete.We have further shown that all these results hold even if doglegging is allowed.We have incorporated the reviewer suggestions to the best of our abilities.

Spanning cactus: Complexity and extensions

Abstract Minimum spanning cactus and minimum spanning cactus extension problems are studied. Both problems are NP-Complete. We present an approximation algorithm for the minimum spanning cactus extension of a forest, a hardness of approximation result of the general minimum spanning cactus problem. For the minimum spanning cactus extension problem, Kabadi and Punnen presented polynomial time algorithms for extending quasi-stars, spanning trees (Kabadi and Punnen, 2013). We present improved analysis of their algorithms in both cases. We further show that their algorithm for the extension of spanning trees can be generalized to extend any connected spanning partial cactus. As a requirement of improved implementation, we have presented a new O ( n 3 ) algorithm to compute all minimum cost monotone paths with respect to a spanning tree.

Approximate spanning cactus

We study minimum spanning cactus and bottleneck spanning cactus problems with ?-triangle inequality. Both problems are NP-Complete. No approximation algorithms are known for these problems. We present ? approximation algorithm for the first and 2 ? - 1 approximation algorithm for the second problem. No approximation algorithms are known for computing minimum spanning cactus and bottleneck spanning cactus.For minimum spanning cactus approximation algorithm with relative error ? is presented.For Bottleneck spanning cactus approximation algorithm with relative error 2 ? - 1 is presented.

Generation of random channel specifications for channel routing problem

In this paper we develop algorithms for generating random channel specifications of channel routing problem in VLSI design. A channel is a rectangular routing region containing two sets of fixed terminals on two of its opposite sides and the other two opposite sides (of the rectangle) are open ends, may or may not contain any terminal of a net but the terminal position is not fixed before a routing solution is computed. Most of the problems in two-, three-, and multi-layer channel routing are beyond polynomial time computable. Hence for each of these problems it is unlikely to design a polynomial time deterministic algorithm. Developing heuristic algorithm might be a probable way out that hopefully provides good solutions for most of the instances occur in practice. Novelty of a heuristic algorithm is judged better if it works for a variety of large number of randomly generated instances of the problem. In fact, convergence of results of a heuristic algorithm is well established when the algorithm of a problem is executed for a huge number of randomly generated similar instances and the final result is computed making an average on all of them.