Using Sifting for k-Layer Straightline Crossing Minimization

Abstract

Abstract. We present a new algorithm for k-layer straightline crossing minimization which is based on sifting that is a heuristic for dynamic reordering of decision diagrams used during logic synthesis and formal verification of logic circuits. The experiments prove sifting to be very efficient. In particular it outperforms the traditional layer by layer sweep based heuristics known from literature by far when applied to k-layered graphs with k ≥ 3.

Crossing Reduction in Circular Layouts

“…Sifting was originally introduced as a heuristic for vertex minimization in ordered binary decision diagrams [11] and later adapted for the one-sided crossing minimization problem [8]. The idea is to keep track of the objective function while moving a vertex along a fixed ordering of all other vertices.…”

“…For the second phase, we adapt a local optimization procedure for layered layouts, sifting [8], to the circular case. Note that, similar to 2-layer layouts, the number of crossing is completely determined by the (cyclic) ordering of vertices.…”

A Parallel Approach to Row-Based VLSI Layout Using Stochastic Hill-Climbing

“…To avoid it, it is possible to simplify the procedure by, for example, removing crossover, simplifying mutation and using a simple evaluation function. Very good results were achieved, better than the best heuristics in this area-sifting [9] and penalty minimization [3]-by mutation reduced to swapping two randomly chosen vertices and by applying hill-climbing using a differential fitness function (only the changed edges were checked), see Algorithm 2. This approach has not been applied before.…”

“…The time for the algorithm to reach the known crossing number was measured. Complete binary trees (an n-level complete binary tree has a bipartite crossing number n 3 − 11 9 2 n + 2 9 (−1) n + 2, see [13]), cycles (with a bipartite crossing number n 2 − 1, if there are n vertices in the cycle) and caterpillars (without crossings in the optimal drawing) have been used to test if the algorithms are working correctly. Rectangular meshes, 3 × n, (with a bipartite crossing number equal to 5n − 6, see [14]) have been used as a more challenging problem than cycles.…”

Recursive bi-partitioning of netlists for large number of partitions

“…The problem of drawing a netlist usually is divided into several subproblems [17,9], like partitioning [10,13], crossing minimization [11,18,19], and level assignment [6]. In most cases only a small fraction of the complete design is shown on the screen.…”