Experimental algorithmics, also referred to as algorithm engineering, is the principled approach of using empirical methods to complement traditional theoretical methods, both of which provide valuable insights for the analysis of algorithms. In this dissertation, we study various algorithmic problems for road networks and noisy sorting, analyzing them from both an experimental and theoretical perspective.

We first study the problem of exact learning for road networks, and introduce an efficient randomized algorithm using simple distance queries, which can find missing roads and improve the quality of routing services. We provide a partial theoretical analysis based on a cluster degree parameter, d_max, then empirically show that this parameter is small for road networks by evaluating our algorithm on road network data for the U.S. and 4 European countries of various sizes. This analysis provides experimental evidence that our algorithm issues a quasilinear number of queries in expectation for road networks and similar graphs. We also study the small-world navigability of the U.S. road network, inspired by the famous experiments done by Stanley Milgram which gave rise to the "six degrees of separation" expression. We introduce the Neighborhood Preferential Attachment Model, and perform extensive experiments with this model on U.S. road networks to show that our model outperforms other small-world models in terms of the average hop length, while having a more realistic scale-free degree distribution.

We then study the problem of sorting n comparable distinct elements, subject to noisy comparison errors, such that the comparison of two elements returns the wrong answer according to a fixed probability p_e > 1/2. We provide new methods for sorting with comparison errors that are data oblivious while avoiding the use of noisy binary search methods. We then experimentally compare our algorithms and other sorting algorithms. Lastly, we study the noisy sorting problem in an external-memory setting, providing new efficient methods that are in the external-memory model for sorting with comparison errors. Our algorithms achieve an optimal number of I/Os, in both cache-aware and cache-oblivious settings.