7 research outputs found
Approximating the generalized terminal backup problem via half-integral multiflow relaxation
We consider a network design problem called the generalized terminal backup
problem. Whereas earlier work investigated the edge-connectivity constraints
only, we consider both edge- and node-connectivity constraints for this
problem. A major contribution of this paper is the development of a strongly
polynomial-time 4/3-approximation algorithm for the problem. Specifically, we
show that a linear programming relaxation of the problem is half-integral, and
that the half-integral optimal solution can be rounded to a 4/3-approximate
solution. We also prove that the linear programming relaxation of the problem
with the edge-connectivity constraints is equivalent to minimizing the cost of
half-integral multiflows that satisfy flow demands given from terminals. This
observation presents a strongly polynomial-time algorithm for computing a
minimum cost half-integral multiflow under flow demand constraints
Discrete Convex Functions on Graphs and Their Algorithmic Applications
The present article is an exposition of a theory of discrete convex functions
on certain graph structures, developed by the author in recent years. This
theory is a spin-off of discrete convex analysis by Murota, and is motivated by
combinatorial dualities in multiflow problems and the complexity classification
of facility location problems on graphs. We outline the theory and algorithmic
applications in combinatorial optimization problems
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
First Annual Workshop on Space Operations Automation and Robotics (SOAR 87)
Several topics relative to automation and robotics technology are discussed. Automation of checkout, ground support, and logistics; automated software development; man-machine interfaces; neural networks; systems engineering and distributed/parallel processing architectures; and artificial intelligence/expert systems are among the topics covered