Professor Apostolico's research interests are in the areas of algorithmic analysis and design and parallel computation. His recent work deals with algorithms and data structures for combinatorial pattern matching problem as arising in text editing, data compression, picture processing, biomolecular sequence analysis, etc. He is a co-editor (with Z. Galil) of the books Combinatorial Algorithms on Words (Springer-Verlag) and Pattern Matching Algorithms (Oxford Univ. Press), serves on the editorial boards of Parallel Processing Letters, Theoretical Computer Science, Journal of Computational Biology, Chaos Theory and Applications, and was guest editor for a special issue of Algorithmica on string algorithms and their applications.

He also serves on the steering committee of the International Symposia on Combinatorial Pattern Matching, the Proceedings of which he co-edited in 1993, 1994, and 1997 on the executive committees of the Fibonacci Institute for the Foundations of Computer Science and of the MSE Program in Software Engineering. He has served on the program committees of many international conferences, most recently, the International Colloquium on Automata, Languages, and Programming, the IEEE Data Compression Conference, the IFIP Conference on Parallel Algorithms for Irregularly Structured Problems, the Workshop on Algorithms and Data Structures, Research in Computational Biology (RECOMB), etc., and as an invited speaker at various international conferences and advanced schools.