This volume constitutes the refereed post-workshop proceedings of the International Workshop on Algorithmic Engineering and Experimentation (ALENEX'99), held in Baltimore, Maryland, USA, in January 1999. The 20 revised full papers presented were carefully selected from a total of 42 submissions during two rounds of reviewing and improvement. The papers are organized into sections on combinatorial algorithms, computational geometry, software and applications, algorithms for NP-hard problems and data structures.

Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a...