Conference
An improved quality hierarchical congestion approximator in near-linear time
| Title: | An improved quality hierarchical congestion approximator in near-linear time |
|---|---|
| Authors: | Henzinger, Monika H, Münk, Robin, Räcke, Harald |
| Source: | Henzinger M, Münk R, Räcke H. An improved quality hierarchical congestion approximator in near-linear time. In: 58th Annual ACM Symposium on Theory of Computing . ACM; 2026:1417-1428. doi: 10.1145/3798129.3800851 |
| Publisher Information: | ACM |
| Publication Year: | 2026 |
| Collection: | IST Austria Research Explorer (Institute of Science and Technology) |
| Subject Terms: | Congestion Approximators, Hierarchical Graph Decompositions, ddc:000 |
| Description: | A single-commodity congestion approximator for a graph is a compact data structure that approximately predicts the edge congestion required to route any set of single-commodity flow demands in a network. A hierarchical congestion approximator (HCA) consists of a laminar family of cuts in the graph and has numerous applications in approximating cut and flow problems in graphs, designing efficient routing schemes, and managing distributed networks. There is a tradeoff between the running time for computing an HCA and its approximation quality. The best polynomial-time construction in an n-node graph gives an HCA with approximation quality O(log1.5n loglogn). Among near-linear time algorithms, the best previous result achieves approximation quality O(log4 n). We improve upon the latter result by giving the first near-linear time algorithm for computing an HCA with approximation quality O(log2 n loglogn). Additionally, our algorithm can be implemented in the parallel setting with polylogarithmic span and near-linear work, achieving the same approximation quality. This improves upon the best previous such algorithm, which has an O(log9n) approximation quality. We also present a lower bound of Ω(logn) for the approximation guarantee of hierarchical congestion approximators. Crucial for achieving a near-linear running time is a new partitioning routine that, unlike previous such routines, manages to avoid recursing on large subgraphs. To achieve the improved approximation quality, we introduce the new concept of border routability of a cut and provide an improved sparsest cut oracle for general vertex weights. |
| Document Type: | conference object report |
| Language: | English |
| ISSN: | 0737-8017 |
| Relation: | info:eu-repo/semantics/altIdentifier/issn/0737-8017; info:eu-repo/semantics/altIdentifier/isbn/9798400725364; info:eu-repo/semantics/altIdentifier/arxiv/2511.03716 |
| Availability: | https://research-explorer.ista.ac.at/record/22245 https://research-explorer.ista.ac.at/download/22245/22250 |
| Rights: | info:eu-repo/semantics/openAccess |
| Accession Number: | edsbas.D5CE735A |
| Database: | BASE |
| ISSN: | 07378017 |
|---|