Experimental Study of Compressed Stack Algorithms in Limited Memory Environments

The compressed stack is a data structure designed by Barba et al. (Algorithmica 2015) that allows to reduce the amount of memory needed by a certain class of algorithms at the cost of increasing its runtime. In this paper we introduce the first implementation of this data structure and make its source code publicly available. Together with the implementation we analyse the performance of the compressed stack. In our synthetic experiments, considering different test scenarios and using data sizes ranging up to 2^{30} elements, we compare it with the classic (uncompressed) stack, both in terms of runtime and memory used. Our experiments show that the compressed stack needs significantly less memory than the usual stack (this difference is significant for inputs containing 2000 or more elements). Overall, with a proper choice of parameters, we can save a significant amount of space (from two to four orders of magnitude) with a small increase in the runtime (2.32 times slower on average than the classic stack). These results hold even in test scenarios specifically designed to be challenging for the compressed stack

Routing on the Visibility Graph

We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of non-crossing line segments whose endpoints are in $P$. We present two deterministic 1-local $O(1)$-memory routing algorithms that are guaranteed to find a path of at most linear size between any pair of vertices of the \emph{visibility graph} of $P$ with respect to a set of constraints $S$ (i.e., the algorithms never look beyond the direct neighbours of the current location and store only a constant amount of additional information). Contrary to {\em all} existing deterministic local routing algorithms, our routing algorithms do not route on a plane subgraph of the visibility graph. Additionally, we provide lower bounds on the routing ratio of any deterministic local routing algorithm on the visibility graph.Comment: An extended abstract of this paper appeared in the proceedings of the 28th International Symposium on Algorithms and Computation (ISAAC 2017). Final version appeared in the Journal of Computational Geometr