Theory of linear and integer programming
Theory of linear and integer programming
General Dynamic Routing with Per-Packet Delay Guarantees of O(Distance + 1/Session Rate)
SIAM Journal on Computing
The Maximum Edge-Disjoint Paths Problem in Bidirected Trees
SIAM Journal on Discrete Mathematics
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Max-Weight Integral Multicommodity Flow in Spiders and High-Capacity Trees
Approximation and Online Algorithms
Conversion of coloring algorithms into maximum weight independent set algorithms
Discrete Applied Mathematics
Packet routing: complexity and algorithms
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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In the periodic packet routing problem a number of tasks periodically create packets which have to be transported through a network. Due to capacity constraints on the edges, it might not be possible to find a schedule which delivers all packets of all tasks in a feasible way. In this case one aims to find a feasible schedule for as many tasks as possible, or, if weights on the tasks are given, for a subset of tasks of maximal weight. In this paper we investigate this problem on trees and grids with row-column paths. We distinguish between direct schedules (i.e., schedules in which each packet is delayed only in its start vertex) and not necessarily direct schedules. For these settings we present constant factor approximation algorithms, separately for the weighted and the cardinality case. Our results combine discrete optimization with real-time scheduling. We use new techniques which are specially designed for our problem as well as novel adaptions of existing methods.