Survivable Network Design: Group Connectivity (Yuhao Zhang)


In the classical survivable network design problem (SNDP), we are given an undirected graph  with costs on edges and a connectivity requirement  for each pair of vertices. The goal is to find a minimum-cost subgraph  such that every pair  are connected by  edge or (openly) vertex disjoint paths, abbreviated as EC-SNDP and VC-SNDP, respectively. The seminal result of Jain [FOCS'98, Combinatorica'01] gives a -approximation algorithm for EC-SNDP, and a decade later, an -approximation algorithm for VC-SNDP, where  is the largest connectivity requirement, was discovered by Chuzhoy and Khanna [FOCS'09, Theory Comput.'12]. While there is a rich literature on point-to-point settings of SNDP, the viable case of connectivity between subsets is still relatively poorly understood.

This paper concerns the generalization of SNDP into the subset-to-subset setting, namely Group EC-SNDP. We develop the framework, which yields the first non-trivial (true) approximation algorithm for Group EC-SNDP. Previously, only a bicriteria approximation algorithm is known for Group EC-SNDP [Chalermsook, Grandoni, and Laekhanukit, SODA'15], and a true approximation algorithm is known only for the single-source variant with connectivity requirement  [Gupta, Krishnaswamy, and Ravi, SODA'10; Khandekar, Kortsarz, and Nutov, FSTTCS'09 and Theor. Comput. Sci.'12].


2022-07-05  13:30 - 14:30   


Yuhao Zhang,  SJTU


Tencent meeting ID: 853-8759-9058; PW: 123456