A new algorithm for compression of partially commutative alphabets

Abstract

In this paper, we will address the problem of how to compress sequences defined in partially commutative alphabets. The use of partial order between symbols may result in far more efficient compression schemes than the most commonly used compression techniques, which use total order. We suggest a new algorithm for compressing sequences defined in alphabets with a partial order. This new algorithm is named the Lempel–Ziv with Partial Order (POLZ) and stands for a Lempel–Ziv (LZ78) generalization. We will show how to compress and decompress sequences by utilizing the POLZ. In addition, we establish the methods for determining the upper bounds for sequence complexity by using the notion of equivalence classes. We will also demonstrate that POLZ is asymptotically optimal, achieving an even greater compression rate when compared to the LZ78 when applied to sequences emanating from concurrent processes. Furthermore, we will show that the complexity obtained by using the LZ78 is also an upper bound for the POLZ complexity. We have developed examples in robotics and real-time systems to show how to use and the benefits of using our algorithm for compression within the context of concurrent systems. When the concurrency of the processes is taken into account, all experimental results show a significant compression gain.