An Experimental Analysis of Change Propagation in Dynamic Trees

Change propagation is a technique for automatically adjusting the output of an algorithm to changes in the input. The idea behind change propagation is to track the dependences between data and function calls, so that, when the input changes, functions affected by that change can be re-executed to update the computation and the output. Change propagation makes it possible for a compiler to dynamize static algorithms. The practical effectiveness of change propagation, however, is not known. In particular, the cost of dependence tracking and change propagation may seem significant. The contributions of the paper are twofold. First, we present some experimental evidence that change propagation performs well when compared to direct implementations of dynamic algorithms. We implement change propagation on tree-contraction as a solution to the dynamic trees problem and present an experimental evaluation of the approach. As a second contribution, we present a library for dynamic-trees that support a general interface and present an experimental evaluation by considering a broad set of applications. The dynamic-trees library relies on change propagation to handle edge insertions/deletions. The applications that we consider include path queries, subtree queries, leastcommon-ancestor queries, maintenance of centers and medians of trees, nearest-marked-vertex queries, semidynamic minimum spanning trees, and the max-flow algorithm of Sleator and Tarjan.