The project achieved several landmark breakthroughs in algorithmic efficiency and theoretical understanding. We developed a comprehensive suite of streaming algorithms, including new results for the k-mismatch problem and near-optimal methods for approximating the Hamming distance in the streaming model. A primary technical highlight was solving a "decade-old" open question by developing the first poly-logarithmic space streaming algorithm for pattern matching under Edit distance.
Furthermore, the project established a wide range of conditional lower bounds that define the computational limits of the field. These include proving the optimality of dynamic LZ77 factorization under the Strong Exponential Time Hypothesis (SETH), showing that update times cannot be improved beyond O(n^2/3). We established hardness results for online dictionary matching with one gap based on the 3SUM conjecture and explored the complexity of set disjointness and intersection with bounded universes. We also provided a breakthrough disproof of the Strong 3SUM-INDEXING Conjecture and established optimal time-space tradeoffs for Color Distance Oracles (CDO) and the "snippets" problem under the APSP hypothesis.
The research also yielded significant results for the biological community, including "GreedyMini," a novel method for generating low-density DNA minimizers , and "FiSSC" (Finding Smallest Sequence Covers), which addresses RNA editing by covering sets of degenerate reads.
Our dissemination efforts included a "Holiday School" and a program on the "Theory of Data Science and Deep Learning". We hosted prominent visitors, including Tatiana A. Starikovskaya, Edo Liberty, Przemek Uznański, Konstantin Makarychev, Jelani Nelson, Tal Wagner, David Woodruff, Omri Weinstein, Jeremy Fineman, David Harris, and Cliff Stein. Results were presented at top-tier conferences such as STOC, FOCS, and SODA.
