In this paper, a novel graph based method for solving a general Applied to IC Layout Compaction and Migration case layout compaction problem is introduced. A new graph representation is proposed. In contrast to previous graph representations, Hazem Said, Hazem M. Abbas, Member, IEEE, Hussein I. the proposed method supports all forms of linear constraints and Shahein linear optimization functions. An algorithm is introduced in which all matrix operations of LP are replaced by fast graph operations on the new graph representation. The method outperforms all the above Abstract-In this paper, a novel method for solving the IC layout . . .compaction problem is introduced. The solution supports all kinds of mentioned methods by combining both the generality of LP and the linear constraints and linear optimization functions. Graph-based tech-efficiency of pure graph-based methods. The details of this algorithm niques are employed so that all matrix operations in linear programming will be discussed in the rest of this paper. In section 2, the problem are replaced by much faster graph operations. The proposed algorithm formulation is introduced. The details of the LP simplex method is outperforms all studied compaction methods by combining the generality of linear programming and the efficiency of graph-based methods.in section 3. The propos gh representai is discused Correct and optimal migrated layouts were produced with significant in section 4. The theoretical basics of the new algorithm is presented improvement in performance.in section 5 followed by the new algorithm in section 6. Section 7 Index Terms-IC layout, Layout Compaction, Linear Programming, contains the results of test cases. The paper is concluded in section Graph Theory.8.
II. PROBLEM FORMULATION I. INTRODUCTIONA valid layout is the one that satisfies certain set of constraints As the technology advances, the need for more compact layout is increasing. The subject of compaction of integrated circuits layout defined by design rules. Most of those constraints are distance ,,, ., constraints that are in the form of x2 -z >3 di3. In addition, more has become a very important aspect of the CAD field. This is due to the need for more dense circuits especially in new technologies. Also, complex constraints like symmetry constraints that are in the form the need for compaction in circuit migration from old technologies X2-XI X4-X3 can be defined by the designer in order to preserve to newer ones is growing. Circuit migration enables the reuse of old matching between two layout elements.The problem of edge-based layout compaction can be formulated circuits in new technologies without the need to redesgn theas a linear programming problem. The formulation used here is: which greatly shortens the layout design cycle.The compaction topic was first introduced in 1970 by Akers [1]. Minimize f =[x Most compaction techniques work on one dimension at a time [2]. Subject to: xj -i > dij V Distance constraints
