Huge Network, Tiny Resources: Power of Adaptivity

Objective

HuNTR investigates how to solve fundamental optimization problems in huge networks using limited resources. In the age of big data, social, web, and biological networks can have billions of edges, making it infeasible to read the entire input. Sublinear-time algorithms address this challenge by examining only a small part of the network while still solving non-trivial optimization problems. Significant progress has recently been made in designing such algorithms. However, with advances in parallel computational models (such as GPU-based, MapReduce, MPC), a natural question arises: How much does adaptivity help in sublinear-time algorithm design? The primary goal of HuNTR is to resolve this question completely for a large set of optimization problems called monotone graph properties. Several fundamental network problems, such as matching, min-cut, max-flow, and reachability, are in this class and have been a center of attention for the research community for the last 6-7 decades. Toward our goal, (1) I will begin with maximum matching, a cornerstone problem in theoretical computer science with rich mathematical structure, efficient algorithms across various models, and, crucially, a testbed for developing new algorithmic techniques. I will build on my recent breakthrough on non-adaptive matching, which marks the first progress in this direction. (2) These results will then be extended to other important monotone properties and will lead the way for a generalized result for the entire monotone class. Taken together, these results will establish adaptivity as a central principle in sublinear computation, advance our understanding of key graph problems, and demonstrate its importance in related models such as cut-query and local computation algorithms, where exploration has only recently begun. The techniques developed here will extend beyond this project, advancing sublinear-time algorithms and providing tools applicable to other sublinear models.