Professor Apostolico's research interests are in the areas of algorithmic analysis and design and applications. His recent work deals with algorithms and data structures for combinatorial pattern matching and discovery problems 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 , International J. of Bioinformatics Research and Applications , Springer-Verlag Lecture Notes on Bioinformatics , and as guest editor for a special issues of Algorithmica , Information Sciences , Journal of Discrete Algorithms , PPL , and TCS .

A founding member of the steering committee of the International Symposia on Combinatorial Pattern Matching , the Proceedings of which he co-edited in 1993, 1994, 1997, 2002, and 2005, he also serves on the steering committees of the International Conferences on Discovery Science , and of the Symposia on String Processing and Information Retrieval. He was founding executive committee member 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, Research in Computational Biology (RECOMB) , Workshop on Algorithms in Bioinformatics (WABI) , IEEE Data Compression Conference , String Processing and Information Retrieval (SPIRE) , Combinatorial Pattern Matching (CPM) , among others, and as an invited speaker at numerous international conferences and advanced research schools.

In his career, Professor Apostolico has held visiting and permanent appointments in the U.S. (CMU, UIUC, Rensselaer, Purdue, IBM) and Europe (U. of Salerno, U. of L' Aquila, U. of Padova, IASI-CNR, U. of Paris, U. of London, King's College, Zif-Bielefeld, Renyi-Hungarian Acad. of Science).  He has been the (co-)recipient of US (Air Force, NIH, NSF, IBM), British, French, Italian, Collaborative (Israel, Korea, Japan), and International (Fulbright, NATO, ESPRIT) research grants.