1 research outputs found
Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity
The terminal backup problems (Anshelevich and Karagiozova (2011)) form a
class of network design problems: Given an undirected graph with a requirement
on terminals, the goal is to find a minimum cost subgraph satisfying the
connectivity requirement. The node-connectivity terminal backup problem
requires a terminal to connect other terminals with a number of node-disjoint
paths. This problem is not known whether is NP-hard or tractable. Fukunaga
(2016) gave a -approximation algorithm based on LP-rounding scheme using a
general LP-solver. In this paper, we develop a combinatorial algorithm for the
relaxed LP to find a half-integral optimal solution in time, where is the number of nodes, is
the number of edges, is the number of terminals, is the maximum
edge-cost, is the maximum edge-capacity, and is
the time complexity of a max-flow algorithm in a network with nodes and
edges. The algorithm implies that the -approximation algorithm for
the node-connectivity terminal backup problem is also efficiently implemented.
For the design of algorithm, we explore a connection between the
node-connectivity terminal backup problem and a new type of a multiflow, called
a separately-capacitated multiflow. We show a min-max theorem which extends
Lov\'{a}sz-Cherkassky theorem to the node-capacity setting. Our results build
on discrete convexity in the node-connectivity terminal backup problem.Comment: A preliminary version of this paper was appeared in the proceedings
of the 47th International Colloquium on Automata, Languages and Programming
(ICALP 2020