Algorithmic strategies in combinatorial chemistry. Combinatorial Chemistry is a powerful new technology in drug design and molecular recognition. It is a wet-laboratory methodology aimed at “massively parallel” screening of chemical compounds for the discovery of compounds that have a certain biological activity. The power of the method comes from the interaction between experimental design and computational modeling. Principles of “rational” drug design are used in the construction of combinatorial libraries to speed up the discovery of lead compounds with the desired biological activity.par This paper presents algorithms, software development and computational complexity analysis for problems arising in the design of combinatorial libraries for drug discovery. We provide exact polynomial time algorithms and intractability results for several Inverse Problems -- formulated as (chemical) graph reconstruction problems -- related to the design of combinatorial libraries. These are the first rigorous algorithmic results in the literature. We also present results provided by our combinatorial chemistry software package OCOTILLO for combinatorial peptide design using real data libraries. The package provides exact solutions for general inverse problems based on shortest-path topological indices. Our results are superior both in accuracy and computing time to the best software reports published in the literature. For 5-peptoid design, the computation is rigorously reduced to an exhaustive search of about $2%$ of the search space; the exact solutions are found in a few minutes.