Fixed-parameter algorithms for unsplittable flow cover - Cristi, Andrés; Mari, Mathieu; Wiese, Andreas (Theory of computing systems, 2020)
The Unsplittable Flow Cover problem (UFP-cover) models the well-studied general caching problem and various natural resource allocation settings. We are given a path with a demand on each edge and a set of tasks, each task being defined by a subpath and a size. The goal is to select a subset of the tasks of minimum cardinality such that on each edge e the total size of the selected tasks using e is at least the demand of e. There is a polynomial time 4-approximation for the problem [Bar-Noy et al., STOC 2000] and also a QPTAS [Höhn et al., ICALP 2014]. In this paper we study fixed-parameter algorithms for the problem. We show that it is W[1]-hard but it becomes FPT if we can slightly violate the edge demands (resource augmentation) and also if there are at most k different task sizes. Then we present a parameterized approximation scheme (PAS), i.e., an algorithm with a running time of f (k) • n O (1) that outputs a solution with at most (1 +)k tasks or assert that there is no solution with at most k tasks. In this algorithm we use a new trick that intuitively allows us to pretend that we can select tasks from OP T multiple times. 2012 ACM Subject Classification Theory of computation → Packing and covering problems; Theory of computation → Fixed parameter tractability Keywords and phrases Unsplittable Flow Cover, fixed parameter algorithms, approximation algorithms Digital Object Identifier 10.4230/LIPIcs.STACS.2020.42