The Space Race: Progress in Algorithm Space Complexity

Abstract

This paper presents the first broad survey of the space complexities of algorithms for important problems in computer science, analyzing more than 800 algorithms for different problem families, and comparing the different algorithms for each of these problem families. The survey reveals the increasing importance of space complexity in recent years and discusses its relationship with time complexity. Our findings reveal an increasing trend in the percentage of algorithm papers that include space complexity analysis. We identify an increasing trend in the percentage of problem families with asymptotic time-space tradeoffs. Additionally, we find that the few problem families that see improvements in space complexity have typically improved at rates faster than the improvement rates of DRAM access speed and DRAM capacity. Under the right conditions, these algorithmic improvements to space complexity can be much more important than hardware improvements when considering computational speedups related to data accesses. This study sheds light on the space complexity of algorithms and contributes to a better understanding of the relationship between time and space complexities. We have also uploaded the space complexity work for this paper to our website, The Algorithm Wiki¹, to serve as a useful resource for theorists and practitioners alike.