Farach-Colton is of Argentine descent, and grew up in South Carolina. While attending medical school, he came out as gay, and met his future husband, with whom he now has twin children. Farach-Colton is an avid Brazilian jiu-jitsu practitioner and received a bronze medal at the 2015 World Master Jiu-Jitsu IBJJF Championship. He obtained his Ph.D. in 1991 from the University of Maryland, College Park under the supervision of Amihood Amir. He was program chair of the 14th ACM-SIAM Symposium on Discrete Algorithms (SODA 2003).
Amir, Amihood; Benson, Gary; Farach, Martin (April 1996), "Let sleeping files lie: pattern matching in Z-compressed files" (PDF), Journal of Computer and System Sciences, 52 (2): 299–307, CiteSeerX 10.1.1.45.6476 , MR 1393996, doi:10.1006/jcss.1996.0023.
Farach, Martin (1997), "Optimal suffix tree construction with large alphabets", 38th Annual Symposium on Foundations of Computer Science, FOCS '97, Miami Beach, Florida, USA, October 19-22, 1997, IEEE Computer Society, pp. 137–143, CiteSeerX 10.1.1.45.4336 , doi:10.1109/SFCS.1997.646102.
Farach, M.; Thorup, M. (April 1998), "String matching in Lempel-Ziv compressed strings", Algorithmica, 20 (4): 388–404, CiteSeerX 10.1.1.45.5484 , MR 1600834, doi:10.1007/PL00009202.
Bender, Michael A.; Farach-Colton, Martin (2000), "The LCA problem revisited" (PDF), in Gonnet, Gaston H.; Panario, Daniel; Viola, Alfredo, LATIN 2000: Theoretical Informatics, 4th Latin American Symposium, Punta del Este, Uruguay, April 10-14, 2000, Proceedings, Lecture Notes in Computer Science, 1776, Springer, pp. 88–94, doi:10.1007/10719839_9.
Charikar, Moses; Chen, Kevin; Farach-Colton, Martin (2004), "Finding frequent items in data streams" (PDF), Theoretical Computer Science, 312 (1): 3–15, CiteSeerX 10.1.1.145.8413 , MR 2045483, doi:10.1016/S0304-3975(03)00400-6. Previously announced in ICALP 2002.
Bender, Michael A.; Demaine, Erik D.; Farach-Colton, Martin (2005), "Cache-oblivious B-trees", SIAM Journal on Computing, 35 (2): 341–358, CiteSeerX 10.1.1.32.4093 , MR 2191447, doi:10.1137/S0097539701389956. Previously announced at FOCS 2000.