Nick Moore
Title: Investigating the role of Randomness and Non-determinism in
space-bounded computations
Project Type: Computer Science
Description:
The basic aim of the project is to understand the use of randomness and
non-determinism in algorithms, in this case a randomised solution for
undirected ST-connectivity, and the effects of randomness on the space
complexity of the solution. More specifically, the project is aimed
towards understanding and implementing a deterministic log-space
algorithm for undirected ST-connectivity.
Preliminary Preparation:
1. A thorough understanding of the undirected ST-connectivity problem.
2. An understanding of space complexity and its associated classes.
3. Preliminary reading on related concepts such as expander graphs,
pseudo-random generators etc.
Minimum Objectives:
1. Understand and implement a randomised algorithm to solve the
undirected ST-connectivity problem in log-space.
2. Find non-trivial classes of directed graphs, on which the algorithm
provably works.
Intermediate Objectives:
1. Find larger classes of directed graphs where some (more complex)
randomised algorithms still works.
2. Examine some existing space-bounded derandomisation techniques.
3. Implement some of these (e.g. zig-zag product expanders) within
reasonable time and space restrictions.
Advanced Objectives:
1. Understand and implement a deterministic algorithm to solve the
undirected ST-connectivity problem in log-space.
References:
Papadimitriou C. (1994). Computational Complexity, Addison-Wesley
Reingold O., Vadhan S., and Wigderson A., Entropy waves, the zig-zag
graph product, and new constant-degree expanders, Ann. of Math., Vol
155, No 1 (2002), 157-187
Aleliunas R. et al. (1979). Random walks, universal traversal sequences,
and the complexity of maze problems in 20th Annual Symposium on
Foundations of Computer Science, pages 218–223, San Juan, Puerto Rico,
29–31 October 1979. IEEE.
Reingold O. (2008). Undirected Connectivity in Log-Space