Center for Discrete Mathematics and Theoretical Computer Science

About: Center for Discrete Mathematics and Theoretical Computer Science is a facility organization based out in Piscataway, New Jersey, United States. It is known for research contribution in the topics: Local search (optimization) & Optimization problem. The organization has 140 authors who have published 175 publications receiving 2345 citations.

An Enhanced Hybrid Genetic Simulated Annealing Algorithm for VLSI Standard Cell Placement

Abstract: A hybrid genetic simulated annealing algorithm is presented for solving the problem of VLSI standard cell placement with up to millions of cells. Firstly,to make genetic algorithm be capable of handling very large scale of standard cell placement, the strategies of small size population, dynamic updating population,and crossover localization are adopted,and the global search and local search of genetic algorithm are coordinated. Then,by introducing hill climbing(HC) and simulated annealing(SA) into the framework of genetic algorithm and the internal procedure of its operators,an effective crossover operator named Net Cycle Crossover and local search algorithms for the placement problem are designed to further improve the evolutionary efficiency of the algorithm and the quality of its placement results. In the algorithm procedure,HC method and SA method focus on array placement and non-array placement respectively. The experimental results on Peko suite3,Peko suite4 and ISPD04 benchmark circuits show that the proposed algorithm can handle array and non-array placements with 10,000 ~ 1,600,000 cells and 10,000 ~ 210,000 cells respectively,and can effectively improve the quality of placement results in a reasonable running time.

On Isomorphisms of Vertex-transitive Graphs

Abstract: The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel results. Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph. Also, we initiate the study for GI and DGI-groups, defined analogously to the concept of CI and DCI-groups.

On Isomorphisms of Vertex-transitive Graphs

Abstract: The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel results. Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph. Also, we initiate the study for GI and DGI-groups, defined analogously to the concept of CI and DCI-groups.

Unified Contamination-Aware Routing Method Considering Realistic Washing Capacity Constraint in Digital Microfluidic Biochips

Abstract: To fully utilize the dynamic reconfigurability of digital microfluidic biochips, most of electrodes would be shared by different droplets. Thus, contaminations caused by liquid residues among droplets are inevitable which lead to lethal errors in bioassays. To remove the contaminations, washing operations are introduced as an essential step to ensure the correctness of bioassay. However, existing works have oversimplified assumptions on the washing droplet’s behavior and constraints which cannot clean all contaminations with erroneous outcomes. Moreover, straightforward integration of washing operations with droplet routing may increase the execution time of a bioassay which is not feasible for timing-critical bioassay. To effectively remove contaminations and minimize the execution time of a bioassay, this article proposes a unified contamination-aware routing method, which addresses the above issues simultaneously. Firstly, we present a top-down scheme to generate candidates of routing paths, then construct a shortest-path model to select desirable routing solution for all subproblems. With a decision diagram of droplets, we further propose an integer linear programming (ILP) formulation to compact the execution time. Finally, contamination removal by washing droplets with realistic washing capacity is considered for all subproblems. Tested on real-life benchmarks, our proposed method can significantly reduce 72% contamination spots and save 11% execution time.

The effect on the spectral radius of r-graphs by grafting or contracting edges

Abstract: Let $\mathcal{H}^{(r)}_n$ be the set of all connected $r$-graphs with given size $n$. In this paper, we investigate the effect on the spectral radius of $r$-uniform hypergraphs by grafting or contracting an edge and then give the ordering of the $r$-graphs with small spectral radius over $\mathcal{H}^{(r)}_n$, when $n\geq 20$.