Mihai Pǎtraşcu: obituary and open problems

Abstract

Mihai Pǎtraşcu, aged 29, passed away on Tuesday June 5, 2012, after a 1.5 year battle with brain cancer. Mihai’s academic career was short but explosive, full of rich and beautiful ideas as witnessed, e.g., in his 20 STOC/FOCS papers. His many interesting papers are available online at: http://people.csail.mit.edu/mip/papers/index.html. Mihai’s talent showed early. In high school he received numerous medals at national (Romanian) and international olympiads including prizes in informatics, physics and applied math. He received gold medals at the International Olympiad in Informatics (IOI) in both 2000 and 2001. He remained involved with olympiads and was elected member of the International Scientific Committee for the International Olympiad of Informatics since 2010. Mihai’s main research area was data structure lower bounds. In data structures we try to understand how we can efficiently represent, access, and update information. Mihai revolutionized and revitalized the lower bound side, in many cases matching known upper bounds. The lower bounds were proved in the powerful cell-probe model that only charges for memory access, hence which captures both RAM and external memory. Already in 2004 [17], as a second year undergraduate student, with his supervisor Erik Demaine as non-alphabetic second author, he broke the Ω(log n/ log log n) lower bound barrier that had impeded dynamic lower bounds since 1989 [6], and showed the first logarithmic lower bound by an elegant short proof, a true combinatorial gem. The important conclusion was that binary search trees are optimal algorithms for the textbook problem of maintaining prefix sums in a dynamic array. They also proved an Ω(log n) lower bound for dynamic trees, matching Sleator and Tarjan’s upper bound from 1983 [20]. In 2005 he received from the Computing Research Association (CRA) the Outstanding Undergraduate Award for best undergraduate research in the US and Canada. I was myself lucky enough to meet Mihai in 2004, starting one of most intense collaborations I have experienced in my career. It took us almost two years to find the first separation between near-linear and polynomial space in data structures [19]. What kept us going on this hard problem was that we always had lots of fun on the side: playing squash, going on long hikes, and having beers celebrating every potentially useful idea we found on the way. A strong friendship was formed. Mihai published more than 10 papers while pursuing his undergraduate studies at MIT from 2002 to 2006. Nevertheless he finished with a perfect 5.0/5.0 GPA. Over the next 2 years, he did his PhD at MIT. His thesis “Lower Bound Techniques for Data Structures” [11] is a must-read for researchers who want to get into data structure lower bounds. During Mihai’s PhD, I got to be his mentor at AT&T, and in 2009, after a year as Raviv Postdoctoral Fellow at IBM Almaden, he joined me at AT&T. We continued our work on lower bounds, but I also managed to get him interested in hashing which is of immense importance to real computing. We sought schemes that were both truly practical and theoretically powerful [15].