Rajat Kumar Pal

Resolving horizontal constraints and minimizing net wire length for multi-layer channel routing

The channel routing problem in VLSI design is to route a specified interconnection among modules in as small an area as possible. Hashimoto and Stevens (1971) proposed an algorithm for solving the two-layer channel routing problem in the absence of vertical constraints. In this paper, we analyze this algorithm in two different ways. In the first analysis, we show that a graph-theoretic realization, algorithm MCC1, runs in O(m + n + e) time, where m is the size of the channel specification of n nets, and e is the size of the complement of the horizontal constraint graph. In the second analysis, algorithm MCC2, we show that a time complexity of O(m + n log n) can be achieved. Algorithms MCC1 and MCC2 guarantee optimum routing solutions under the multi-layer V/sub i+1/H/sub i/ (i/spl ges/1) routing model, where the horizontal and vertical layers of interconnect alternate. Finally, we consider the problem of minimizing the total net wire length in the V/sub i+1/H/sub i/ (i/spl ges/1) routing model. Given a channel specification and a partition of the set of nets (where the nets within each part of the partition are non-overlapping), we propose an O(m + d/sub max/log d/sub max/) time algorithm for minimizing the total net wire length, subject to the condition that nets from a part of the partition are assigned to the same track. All our solutions use the minimum number of via holes.<<ETX>>

An efficient genetic algorithm for multi-objective solid travelling salesman problem under fuzziness

Abstract In this paper, we have presented a multi-objective solid travelling salesman problem (TSP) in a fuzzy environment. The attraction of the solid TSP is that a traveller visits all the cities in his tour using multiple conveyance facilities. Here we consider cost and time as two objectives of the solid TSP. The objective of the study is to find a complete tour such that both the total cost and the time are minimized. We consider travelling costs and times for one city to another using different conveyances are different and fuzzy in nature. Since cost and time are considered as fuzzy in nature, so the total cost and the time for a particular tour are also fuzzy in nature. To find out Pareto-optimal solution of fuzzy objectives we use fuzzy possibility and necessity measure approach. A multi-objective genetic algorithm with cyclic crossover, two-point mutation, and refining operation is used to solve the TSP problem. In this paper a multi-objective genetic algorithm has been modified by introducing the refining operator. Finally, experimental results are given to illustrate the proposed approach; experimental results obtained are also highly encouraging.

A general graph theoretic framework for multi-layer channel routing

In this paper we propose a general framework for viewing a class of heuristics for track assignment in channel routing from a purely graph theoretic angle. Within this framework we propose algorithms for computing routing solutions using optimal or near optimal number of tracks for several well-known benchmark channels in the two-layer VH. Three-layer HVH, and multi-layer V/sub i/H/sub i/ and V/sub i/H/sub i+1/ routing models. Within the same framework we also design an algorithm for minimizing the total wire length in the two-layer VH and three-layer HVH routing models.

An Ant colony optimization approach for binary knapsack problem under fuzziness

In this paper, we represent a novel ant colony optimization algorithm to solve binary knapsack problem. In the proposed algorithm for n objects, n candidate groups are created, and each candidate group has exactly m values (for m ants) as 0 or 1. For each candidate value in each group a pheromone is initialized by the value between 0.1 and 0.9, and each ant selects a candidate value from each group. Therefore, the binary solution is generated by each ant by selecting a value from each group. In each generation, pheromone update and evaporation is done. During the execution of algorithm after certain number of generation the best solution is stored as a temporary population. After that, crossover and mutation is performed between the solution generated by ants. We consider profit and weight are fuzzy in nature and taken as trapezoidal fuzzy number. Fuzzy possibility and necessity approaches are used to obtain optimal decision by the proposed ant colony algorithm. Computational experiments with different set of data are given in support of the proposed approach.

All-optical binary to gray code and gray to binary code conversion scheme with the help of semiconductor optical amplifier-assisted sagnac switch

Gray codes are widely used to facilitate error correction in digital communications. An all-optical four-bit binary to Gray code and Gray to binary code converter with the help of semiconductor optical amplifier-assisted Sagnac switch is proposed and described. This study describes all-optical conversion scheme using a set of all-optical switches. The new method promises both higher processing speed and accuracy. Numerical simulation result confirming the described methods and conclusion are given here.

All-optical adder/subtractor based on terahertz optical asymmetric demultiplexer

An all-optical adder/subtractor (A/S) unit with the help of terahertz optical asymmetric demultiplexer (TOAD) is proposed. The all-optical A/S unit with a set of all-optical full-adders and optical exclusive-ORs (XORs), can be used to perform a fast central processor unit using optical hardware components. We try to exploit the advantages of TOAD-based optical switch to design an integrated all-optical circuit which can perform binary addition and subtraction. With computer simulation results confirming the described methods, conclusions are given.

Engineered Silybin Nanoparticles Educe Efficient Control in Experimental Diabetes

Silybin, is one imminent therapeutic for drug induced hepatotoxicity, human prostrate adenocarcinoma and other degenerative organ diseases. Recent evidences suggest that silybin influences gluconeogenesis pathways favorably and is beneficial in the treatment of type 1 and type 2 diabetes. The compound however is constrained due to solubility (0.4 mg/mL) and bioavailabilty limitations. Appropriate nanoparticle design for silybin in biocompatible polymers was thus proposed as a probable solution for therapeutic inadequacy. New surface engineered biopolymeric nanoparticles with high silybin encapsulation efficiency of 92.11% and zeta potential of +21 mV were designed. Both the pure compound and the nanoparticles were evaluated in vivo for the first time in experimental diabetic conditions. Animal health recovered substantially and the blood glucose levels came down to near normal values after 28 days treatment schedule with the engineered nanoparticles. Restoration from hyperglycemic damage condition was traced to serum insulin regeneration. Serum insulin recovered from the streptozotocin induced pancreatic damage levels of 0.17±0.01 µg/lit to 0.57±0.11 µg/lit after nanoparticle treatment. Significant reduction in glycated hemoglobin level, and restoration of liver glycogen content were some of the other interesting observations. Engineered silybin nanoparticle assisted recovery in diabetic conditions was reasoned due to improved silybin dissolution, passive transport in nanoscale, and restoration of antioxidant status.

All-Optical Binary-Coded Decimal Adder with a Terahertz Optical Asymmetric Demultiplexer

In electronic computing systems, the binary-coded decimal (BCD) method encodes decimal numbers with each digit represented by its own four-bit binary sequence. The method allows easy conversion to decimal digits for printing or display and also offers rapid decimal calculations. A proposed all-optical BCD adder uses a terahertz optical asymmetric demultiplexer (TOAD) to perform BCD addition in all-optical domain.

A time-optimal algorithm for guard zone problem

Given a simple polygon P, its guard zone G (of width r) is a closed region consisting of straight line segments and circular arcs (of radius r) bounding the polygon P such that there exists no pair of points p (on the boundary of P) and q (on the boundary of G) having their Euclidean distance d(p,q) less than r. In this paper we have designed a time-optimal sequential algorithm to solve the guard zone problem.

A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment

In this paper, a genetic-ant colony optimization algorithm has been presented to solve a solid multiple Travelling Salesmen Problem (mTSP) in fuzzy rough environment. In solid mTSP, a set of nodes (locations/cities) are given, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot using different conveyance facility. A solid mTSP is an extension of mTSP where the travellers use different conveyance facilities for travelling from one city to another. To solve an mTSP, a hybrid algorithm has been developed based on the concept of two algorithms, namely genetic algorithm (GA) and ant colony optimization (ACO) based algorithm. Each salesman selects his/her route using ACO and the routes of different salesmen (to construct a complete solution) are controlled by the GA. Here, a set of simple ACO characteristics have further been modified by incorporating a special feature namely ‘refinement’. In this paper, we have utilized cyclic crossover and two-point’s mutation in the proposed algorithm to solve the problem. The travelling cost is considered as imprecise in nature (fuzzy-rough) and is reduced to its approximate crisp using fuzzy-rough expectation. Computational results with different data sets are presented and some sensitivity analysis has also been made.