Periodic Reporting for period 2 - DynASoAr (Dynamic Algorithms Against Strong Adversaries)
Berichtszeitraum: 2023-03-01 bis 2024-08-31
In this project we perform basic research in the area of dynamic graph algorithms. Traditionally, an algorithm is a sequence of instructions for solving a computational problem by transforming the given input data to the desired, problem-specific, output. Under the dynamic algorithms paradigm, we allow the input to be dynamic by undergoing a sequence of changes. The dynamic algorithm processes theses changes one by one and needs to quickly update its output to match the current state of the input. The dynamic setting occurs naturally in many applications and addressing it explicitly can lead to smaller running times in such applications, which in turn has the potential of decreasing resource consumption in computing.
The specific issue address in this project is the following: many existing dynamic algorithms make assumptions on how the sequence of updates is generated. Several dynamic algorithms for example do not allow the next update to depend on the previous outputs of the algorithm. Such assumptions are prohibitive in many applications and therefore this project aims at developing a stronger theory of dynamic algorithms avoiding such assumptions.
The specific issue address in this project is the following: many existing dynamic algorithms make assumptions on how the sequence of updates is generated. Several dynamic algorithms for example do not allow the next update to depend on the previous outputs of the algorithm. Such assumptions are prohibitive in many applications and therefore this project aims at developing a stronger theory of dynamic algorithms avoiding such assumptions.
So far, the team has focused on developing new dynamic algorithms for estimating distances in networks undergoing insertions and/or deletions of links. The main results are dynamic algorithms with nearly optimal update times for maintaining (a) a high-precision estimate if both insertions and deletions are allowed and (b) a low-precision estimate in the insertions-only setting. Furthermore, we have obtained dynamic results for finding clusters in data, which is a central task in unsupervised learning. All of these results have been or will be presented at the most prestigious conferences in the field.
There are still several well-studied fundamental problems for which the "gold standard" of efficient dynamic algorithms that are additionally assumption-free has not been reached. We expect to meet this standard for some of these problems by developing and refining algorithmic techniques. We further expect to obtain more results related to dynamic graph clustering.