Recent directions in netlist partitioning: a survey

This paper introduces and demonstrates an extension to quadratic placement that accounts for wiring congestion. The algorithm uses an A* router and line-probe heuristics on region-based routing graphs to compute routing cost. The interplay between routing analysis and quadratic placement using a growth matrix permits global treatment of congestion. Further reduction in congestion is obtained by the relaxation of pin constraints. Experiments show improvements in wireability.

Congestion driven quadratic placement

Typical placement objectives involve reducing net-cut cost or minimizing wirelength. Congestion minimization is least understood, however, it models routability most accurately. In this paper, we study the congestion minimization problem during placement. First we point out that the bounding box router used previously is not an accurate measurement of the congestion in the placement. We use a realistic global router to evaluate congestion in the placement stage. This ensures that the final placement is truely congestion minimized. We also propose two new post processing algorithms, the flow-based cell-centric algorithm and the net-centric algorithm. While the flow-based cell-centric algorithm can move multiple cells at the same time to minimize the congestion, it suffers large consumption of memory. Experimental results show that the net-centric algorithm can effectively identify the congested spots in the placement and reduce the congestion. It can produce on an average 7.7% less congestion than the bounding box router method. Finally, we use a final global router to verify that the placement obtained from our algorithm has 39% less congestion than a wirelength-optimized placement obtained by TimberWolf (commercial version 1.3.1).

/pdf/modeling-and-minimization-of-routing-congestion-w3bggvdjes.pdf

Modeling and minimization of routing congestion

This dissertation focuses on computing high-quality solutions for the NP-hard balanced hypergraph partitioning problem: Given a hypergraph and an integer $k$, partition its vertex set into $k$ disjoint blocks of bounded size, while minimizing an objective function over the hyperedges. Here, we consider the two most commonly used objectives: the cut-net metric and the connectivity metric.

Since the problem is computationally intractable, heuristics are used in practice - the most prominent being the three-phase multi-level paradigm: During coarsening, the hypergraph is successively contracted to obtain a hierarchy of smaller instances. After applying an initial partitioning algorithm to the smallest hypergraph, contraction is undone and, at each level, refinement algorithms try to improve the current solution.

With this work, we give a brief overview of the field and present several algorithmic improvements to the multi-level paradigm. Instead of using a logarithmic number of levels like traditional algorithms, we present two coarsening algorithms that create a hierarchy of (nearly) $n$ levels, where $n$ is the number of vertices. This makes consecutive levels as similar as possible and provides many opportunities for refinement algorithms to improve the partition. This approach is made feasible in practice by tailoring all algorithms and data structures to the $n$-level paradigm, and developing lazy-evaluation techniques, caching mechanisms and early stopping criteria to speed up the partitioning process. Furthermore, we propose a sparsification algorithm based on locality-sensitive hashing that improves the running time for hypergraphs with large hyperedges, and show that incorporating global information about the community structure into the coarsening process improves quality. Moreover, we present a portfolio-based initial partitioning approach, and propose three refinement algorithms. Two are based on the Fiduccia-Mattheyses (FM) heuristic, but perform a highly localized search at each level. While one is designed for two-way partitioning, the other is the first FM-style algorithm that can be efficiently employed in the multi-level setting to directly improve $k$-way partitions. The third algorithm uses max-flow computations on pairs of blocks to refine $k$-way partitions. Finally, we present the first memetic multi-level hypergraph partitioning algorithm for an extensive exploration of the global solution space.

All contributions are made available through our open-source framework KaHyPar. In a comprehensive experimental study, we compare KaHyPar with hMETIS, PaToH, Mondriaan, Zoltan-AlgD, and HYPE on a wide range of hypergraphs from several application areas. Our results indicate that KaHyPar, already without the memetic component, computes better solutions than all competing algorithms for both the cut-net and the connectivity metric, while being faster than Zoltan-AlgD and equally fast as hMETIS. Moreover, KaHyPar compares favorably with the current best graph partitioning system KaFFPa - both in terms of solution quality and running time.

pdf/high-quality-hypergraph-partitioning-2mltz6h57n.pdf

High-Quality Hypergraph Partitioning

A program and underlying algorithms are described which quasi-optimally partition a set of logic equations into subsets which represent physical packaging entities. The criterion for partitioning is the signal communication between equations. Several different methods of measuring and evaluating the criterion are built into the program as optional strategies. The effectiveness of these and other strategies are compared, based on accumulated experience with the program. The important characteristics of the program and its data structures which allow very efficient computer execution time are described. The plans and techniques for further development of the program are also presented.

Logic partitioning

Placement is an important constrained optimization problem in the design of very large scale
(VLSI) integrated circuits [1–4]. Simulated annealing [5] and min-cut placement [6] are two
of the most successful approaches to the placement problem. Min-cut methods yield less
congested and more routable placements at the expense of more wire-length, while simulated
annealing methods tend to optimize more the total wire-length with little emphasis on the
minimization of congestion. It is also well known that min-cut algorithms are substantially
faster than simulated-annealing-based methods. In this paper, a fast min-cut algorithm
(ROW-PLACE) for row-based placement is presented and is empirically shown to achieve
simulated-annealing-quality wire-length on a number of benchmark circuits. In comparison
with Timberwolf 6 [7], ROW-PLACE is at least 12 times faster in its normal mode and is at
least 25 times faster in its faster mode. The good results of ROW-PLACE are achieved using
a very effective clustering-based partitioning algorithm in combination with constructive
methods that reduce the wire-length of nets involved in terminal propagation.

/pdf/a-fast-clustering-based-min-cut-placement-algorithm-with-56s0az3pam.pdf

A Fast Clustering-Based Min-Cut Placement Algorithm with Simulated-Annealing Performance

Partitioning is a fundamental problem in the design of VLSI circuits. In recent years, themulti-level partitioning approach has been used with success by a number ofresearchers. This paper describes a new multi-level partitioning algorithm (PART) thatcombines a blend of iterative improvement and clustering, biasing of node gains, andlocal uphill climbs. PART is competitive with recent state-of-the-art partitioningalgorithms. PART was able to find new lower cuts for many benchmark circuits. Undersuitably mild assumptions, PART also runs in linear time.

/pdf/a-new-2-way-multi-level-partitioning-algorithm-tqs0k2o2iz.pdf

A New 2-way Multi-level Partitioning Algorithm*

We present an effective solution to the linear placement problem, which has several applications in the physical design of integrated circuits. Our approach belongs to the class of iterative improvement heuristics. The important difference of this new technique from the previous ones is in its moves, and in the order of application of these moves. A phase of the algorithm begins with simple moves and gradually shifts towards more complex moves. Phases are repeated as long as further improvement is possible. Our experimental results show that nearly optimal solutions can be achieved. For a number of examples collected from the literature, our algorithm generated optimal solutions.

/pdf/an-effective-solution-to-the-linear-placement-problem-2eje216atf.pdf

An Effective Solution to the Linear Placement Problem

Partitioning is a fundamental problem in the design of VLSI circuits. In recent years, ratio-cut partitioning has received attention due to its tendency to partition circuits into their natural clusters. Node contraction has also been shown to enhance the performance of iterative partitioning algorithms. This paper describes a new simple ratio-cut partitioning algorithm using node contraction. This new algorithm combines iterative improvement with progressive cluster formation. Under suitably mild assumptions, the new algorithm runs in linear time. It is also shown that the new algorithm compares favorably with previous approaches.

/pdf/a-contraction-based-ratio-cut-partitioning-algorithm-i6cw5ngzyb.pdf

A Contraction-based Ratio-cut Partitioning Algorithm

Partitioning is an important problem in the design automation of integrated circuits. This problem in many of itsformulation is NP-Hard, and several heuristic methods have been proposed for its solution. To evaluate theeffectiveness of the various partitioning heuristics, it is desirable to have test cases with known optimal solutionsthat are as “random looking” as possible. In this paper, we describe several methods for the construction of suchtest cases. All our methods except one use the theory of network flow. The remaining method uses a relationshipbetween a partitioning problem and the geometric clustering problem. The latter problem can be solved inpolynomial time in any fixed dimension.

https://downloads.hindawi.com/journals/vlsi/1995/081535.pdf

New Methods for the Construction of Test Cases for Partitioning Heuristics

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