Showing papers by "Center for Discrete Mathematics and Theoretical Computer Science published in 2020"

An Improved Simulated Annealing Algorithm With Excessive Length Penalty for Fixed-Outline Floorplanning

Abstract: In addition to wirelength and area, modern floorplans need to consider various constraints such as fixed-outline. To handle the fixed-outline floorplanning optimization problem efficiently, we propose an improved simulated annealing (SA) algorithm, which optimizes the area, the total wirelength, and the prescribed outline constraints at the same time. In order to enhance the effectiveness of SA algorithm, we propose a novel feasible solution strategy which ensures that viable solution would be found at all times. Moreover, we propose a new penalty function to better solve the prescribed outline constraint. It consists of a violation area function to prevent modules from moving to the prescribed outline, and an excessive violation function to enable the modules to move close to the optimal positions. Experimental results show that the proposed algorithm is effective and efficient to obtain a fixed-outline floorplan, and achieves a 100% success rate on each benchmark in different aspect ratios.

Commercial Transport During a Pandemic: Network Analysis to Reconcile COVID-19 Diffusion and Vital Supply Chain Resilience.

Abstract: P opulation mobility and transportation are critically linked with the acquisition and spread of infectious diseases. As the nearly two million US long-haul truck drivers traverse vast distances and interact with numerous individuals, they unavoidably render themselves and the populations they intermingle with vulnerable to contracting and spreading re/emerging infections, including coronavirus 2019 (COVID-19). The current COVID-19 pandemic has underscored how little is known about the potential role and consequences of commercial drivers’ social and spatial networks in the heterogeneous acquisition and transmission of such afflictions, as well as the corresponding impacts of these afflictions on the health and safety of transportation workers and on the capacity of critical supply chains. When considering the potential role of long-haul truck drivers in the spread and control of COVID-19, policymakers are faced with a dilemma. On the one hand, the aforementioned risks of COVID-19 acquisition and transmission suggest that public health strategies (eg, shelter-in-place orders) are urgently needed to reduce the potential threat of disease spread via longhaul truck drivers. On the other hand, highly publicized shortages of key medical equipment have magnified the critical service that long-haul truck drivers provide during the pandemic. Because of this, the vital importance of keeping these drivers ‘‘on the road’’ to continue supplying

Hamiltonian Path Based Mixed-Cell-Height Legalization for Neighbor Diffusion Effect Mitigation*

Abstract: In modern circuit designs, standard cells are designed with different heights based on the power, area, and other characteristics to address various design requirements. For those cells with different heights, in particular, there are inter-cell diffusion steps if the diffusion heights of neighboring cells are different, called the neighbor diffusion effect (NDE) which has become critical in advanced technology nodes. In this paper, we present a Hamiltonian-path-based mixed-cell-height legalization algorithm for NDE mitigation. We first present a row assignment method considering both cell displacements and diffusion steps to assign cells to their desired rows that meet the power-rail alignment constraints. Then, we propose a Hamiltonian-path-based diffusion-step reduction method to effectively reduce the NDE violations while preserving the global placement solution. Particularly, we develop a 2-approximation algorithm to find a minimum weight Hamiltonian path connecting two vertices, and a 1.5-approximation algorithm to find a minimum weight Hamiltonian path with a specified end vertex. Finally, we present an NDE-aware legalization method with design compaction to resolve overlaps and NDE violations. Experimental results show that our algorithm can resolve all NDE violations without any area overhead in reasonable runtime.

Block diagonal dominance-based dynamic programming for detecting community

Abstract: Clustering or partition is a fundamental work for graph or network. Detecting communities is a typical clustering, which divides a network into several parts according to the modularity. Community detection is a critical challenge for designing scalable, adaptive and survivable trust management protocol for a community of interest-based social IoT system. Most of the existed methods on community detection suffer from a common issue that the number of communities should be prior decided. This urges us to estimate the number of communities from the data by some way. This paper concurrently considers eliminating the number of communities and detecting communities based on block diagonal dominace adjacency matrix. To construct a block diagonal dominance adjacency matrix for the input network, it first reorders the node number by the breadth-first search algorithm. For the block diagonal dominance adjacency matrix, this paper shows that the numbers of nodes in a community should be continuous adjacent. And thus, it only needs insert some breakpoints in node number sequence to decide the number of communities and the nodes in every community. In addition, a dynamic programming algorithm is designed to achieve an optimal community detection result. Experimental results on a number of real-world networks show the effectiveness of the dynamic programming approach on the community detection problem.

An Efficient EPIST Algorithm for Global Placement with Non-Integer Multiple-Height Cells *

Abstract: With the increasing design requirements of modern circuits, a standard-cell library often contains cells of different row heights to address various trade-offs among performance, power, and area. However, maintaining all standard cells with integer multiples of a single-row height could cause some area overheads and increase power consumption. In this paper, we present an analytical placer to directly consider a circuit design with non-integer multiple-height standard cells and additional layout constraints. The region of different cell heights is adaptively generated by the global placement result. In particular, an exact penalty iterative shrinkage and thresholding (EPIST) algorithm is employed to efficiently optimize the global placement problem. The convergence of the algorithm is proved, and the acceleration strategy is proposed to improve the performance of our algorithm. Compared with the state-of-the-art works, experimental results based on the 2017 CAD Contest at ICCAD benchmarks show that our algorithm achieves the best wirelength and area for every benchmark. In particular, our proposed EPIST algorithm provides a new direction for effectively solving large-scale nonlinear optimization problems with non-smooth terms, which are often seen in real-world applications.

Late Breaking Results: An Analytical Timing-Driven Placer for Heterogeneous FPGAs *

Abstract: As the feature sizes keep shrinking, interconnect delays have become a major limiting factor for FPGA timing closure. Traditional placement algorithms that address wirelength alone are no longer sufficient to close timing, especially for the large-scale heterogeneous FPGAs. In this paper, we resolve the crucial FPGA placement problem by optimizing wirelength and timing simultaneously. First, a smoothed routing-architecture-aware timing model is proposed to accurately estimate each interconnect delay. Then, a timing-driven delay look-up table is constructed to further speed up delay access. Finally, we present an effective wirelength and timing co-optimization strategy to produce high-quality placements without timing violations. Compared with Vivado 2019.1 on Xilinx benchmark suites for xc7k325t device, experimental results show that our algorithm achieves not only a 6.6% improvement in worst slack but also a 3.2% reduction for routed wirelength.

On the α-spectra of Uniform Hypergraphs and Its Associated Graphs

Abstract: For 0 ≤ α < 1 and a k-uniform hypergraph H, the tensor Aα(H) associated with H is defined as Aα(H) = αD(H) + (1 − α)A(H), where D(ℋ) and A(H) are the diagonal tensor of degrees and the adjacency tensor of H, respectively. The α-spectra of H is the set of all eigenvalues of Aα(H) and the α-spectral radius ρα(H) is the largest modulus of the elements in the spectrum of Aα(H). In this paper we define the line graph L(H) of a uniform hypergraph H and prove that $${\rho _\alpha}\left(H \right)\, \le {1 \over \kappa}{\rho _\alpha}\left({L\left(H \right)} \right) + 1 + \alpha \left({{\rm{\Delta}} - 1 - {{{\delta^*}} \over k}} \right)$$ , where Δ and δ* are the maximum degree of H and the minimum degree of L(H), respectively. We also generalize some results on α-spectra of Gk,s, which is obtained from G by blowing up each vertex into an s-set and each edge into a k-set where 1 ≤ s ≤ k/2.

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.

Weighted thresholding homotopy method for sparsity constrained optimization

Abstract: We propose in this paper a novel weighted thresholding method for the sparsity-constrained optimization problem. By reformulating the problem equivalently as a mixed-integer programming, we investigate the Lagrange duality with respect to an $$l_1$$-norm constraint and show the strong duality property. Then we derive a weighted thresholding method for the inner Lagrangian problem, and analyze its convergence. In addition, we give an error bound of the solution under some assumptions. Further, based on the proposed method, we develop a homotopy algorithm with varying sparsity level and Lagrange multiplier, and prove that the algorithm converges to an L-stationary point of the primal problem under some conditions. Computational experiments show that the proposed algorithm is competitive with state-of-the-art methods for the sparsity-constrained optimization problem.

Complex Placement Region Handling Based on Electrostatic System Modeling

Abstract: With the additional fence region constraints in modern circuit designs, the VLSI placement problem has become more complex and challenging. A placement solution without considering fence region constraints may cause many problems in the legalization stage and result in an inferior placement. In this paper, we present an effective placement region handling method based on the two-dimensional electrostatic system modeling. Under the fence region constrains, we first generate multiple density maps for assigning cells to their respective fence regions. Then, we further add proper fence filler nodes to each density map, which is able to squeeze fence cells to be placed closer. The placement performance is validated through experiments on ISPD 2015 benchmarks. Experimental results show that, compared with the state-of-the-art placer NTUplace4dr, our proposed method not only reduces the wirelength by 9.9% but also achieves 5x faster runtime.

Sparse Group Feature Selection by Weighted Thresholding Homotopy Method

Abstract: In this paper, we investigate the sparse group feature selection problem, in which covariates posses a grouping structure sparsity at the level of both features and groups simultaneously. We reformulate the feature sparsity constraint as an equivalent weighted $l_1$ -norm constraint in the sparse group optimization problem. To solve the reformulated problem, we first propose a weighted thresholding method based on a dynamic programming algorithm. Then we improve the method to a weighted thresholding homotopy algorithm using homotopy technique. We prove that the algorithm converges to an $L$ -stationary point of the original problem. Computational experiments on synthetic data show that the proposed algorithm is competitive with some state-of-the-art algorithms.