In this paper, we present the first amortized linear-time packing algorithm for the placement with symmetry constraints. We first introduce the concept of a symmetry island which is formed by modules of the same symmetry group in a single connected placement. Based on this concept and the B*-tree representation, we propose automatically symmetric-feasible B*-trees (ASF-B*-trees) to directly model the placement of a symmetry island. Unlike the previous works that can handle only 1D symmetry constraints, our ASF-B*-tree is the first in the literature to additionally consider 2D symmetry. We then present hierarchical B*-trees (HB*-trees) which can simultaneously optimize the placement with both symmetry islands and non-symmetry modules. Unlike the previous works, our approach can guarantee the close proximity of symmetry modules and significantly reduce the search space based on the symmetry-island formulation. In particular, the packing time for an ASF-B*-tree or an HB*-tree is the same as that for a plain B*-tree (only amortized linear) and much faster than previous works which need at least loglinear time. Experimental results show that our approach achieves the best published quality and runtime efficiency for analog placement.

This paper describes a GA for job shop scheduling problems. Using the Giffler and Thompson algorithm, we created two new operators, THX crossover and mutation, which better transmit temporal relationships in the schedule. The approach produced excellent results on standard benchmark job shop scheduling problems. We further tested many models and scales of parallel GAs in the context of job shop scheduling problems. In our experiments, the hybrid model consisting of coarse-grain GAs connected in a fine-grain-GA-style topology performed best, appearing to integrate successfully the advantages of coarse-grain and fine-grain GAs.

In analog layout design, it is very important to reduce the parasitic coupling effects and improve the circuit performance. Consequently, the most important device-level placement constraints are matching, symmetry, and proximity. However, many previous works deal with these constraints separately, and none of them mention how to handle different constraints simultaneously and hierarchically. In this paper, we first give a case study to show the needs of integrating these constraints in a hierarchical manner. Then, we present the first formulation for analog placement based on hierarchical module clustering. Our approach can handle analog placement with various constraint groups including matching, (hierarchical) symmetry, and (hierarchical) proximity groups. To our best knowledge, this is also the first work in the literature to handle floorplanning with the clustering constraint using the B*-tree based representation. Experimental results based on industrial analog designs show that our approach is very effective and efficient.

Abstract-Due to its great flexibility, gridless routing is desirable for nanometer circuit designs that use variable wire widths and spacings. Nevertheless, it is much more difficult than grid-based routing because of its larger solution space. In this paper, we present a novel "V-shaped" multilevel framework (called VMF) for full-chip gridless routing. Unlike the traditional "Λ-shaped" multilevel framework (inaccurately called the "Vcycle" framework in the literature), our VMF works in the V-shaped manner: top-down uncoarsening followed by bottom-up coarsening. Based on the novel framework, we develop a multilevel full-chip gridless router (called VMGR) for large-scale circuit designs. The top-down uncoarsening stage of VMGR starts from the coarsest regions and then processes down to finest ones level by level; at each level, it performs global pattern routing and detailed routing for local nets and then estimate the routing resource for the next level. Then, the bottom-up coarsening stage performs global maze routing and detailed routing to reroute failed connections and refine the solution level by level from the finest level to the coarsest one. We employ a dynamic congestion map to guide the global routing at all stages and propose a new cost function for congestion control. Experimental results show that VMGR achieves the best routability among all published gridless routers based on a set of commonly used MCNC benchmarks. Besides, VMGR can obtain significantly less wirelength, smaller critical path delay, and smaller average net delay than the previous works. In particular, VMF is general and thus can readily apply to other problems.

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