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Circle graphs are an important class of graph with applications in a number of areas, including compiler optimization, VLSI design and computational geometry. In this article, we provide an experimental evaluation of the two most efficient algorithms for computing the maximum independent set of a circle graph. We provide details of our implementations of the algorithms of Apostolico et al. and Valiente [2003], together with time, space, and other measurements. We describe optimizations to the algorithm of Apostolico et al. that significantly reduce both its running time and its memory consumption. We also correct an error in this algorithm. In addition, we show how to restructure and simplify Valiente's algorithm, allowing us to remove redundant computations from the algorithm resulting in much improved performance. Moreover, in the case of both algorithms, when the density of the circle graph's associated interval representation is increased beyond a certain point the efficacy of the optimizations we apply increases dramatically and as a function of the density. We provide experimental results over dense and sparse random circle graphs, as well as for circle graphs that arise when performing register allocation of software pipelined loops in a compiler.

In this paper, we focus on the register allocation phase of software pipelining. We axe interested in optimal register allocation. This means that the number of registers used must be equal to the maximum number of simultaneously alive variables of the loop. Usually two different means are used to achieve this, namely register renaming or loop unrolling. As these methods have both drawbacks, we introduce here a solution which is a trade-off between inserting m o v e operations and unrolling the modulo-scheduled loop body. We present a new algorithmic framework of optimal register allocation for modulo scheduled loops. The proposed algorithm, called U&M, is simple and efficient. We have implemented it in MOST. An experimental study of our algorithm on more than 1000 loops has been performed and we report a summary of the main results. This new algorithm performs consistently better than several other existing methods.