TY - GEN
T1 - Approximating generalized network design under (Dis)economies of scale with applications to energy efficiency
AU - Emek, Yuval
AU - Lavi, Ron
AU - Kutten, Shay
AU - Shi, Yangguang
N1 - Publisher Copyright: © 2018 Association for Computing Machinery.
PY - 2018/6/20
Y1 - 2018/6/20
N2 - In a generalized network design (GND) problem, a set of resources are assigned (non-exclusively) to multiple requests. Each request contributes its weight to the resources it uses and the total load on a resource is then translated to the cost it incurs via a resource specific cost function. Motivated by energy efficiency applications, recently, there is a growing interest in GND using cost functions that exhibit (dis)economies of scale ((D)oS), namely, cost functions that appear subadditive for small loads and superadditive for larger loads. The current paper advances the existing literature on approximation algorithms for GND problems with (D)oS cost functions in various aspects: (1) while the existing results are restricted to routing requests in undirected graphs, identifying the resources with the graph’s edges, the current paper presents a generic approximation framework that yields approximation results for a much wider family of requests (including various types of Steiner tree and Steiner forest requests) in both directed and undirected graphs, where the resources can be identified with either the edges or the vertices; (2) while the existing results assume that a request contributes the same weight to each resource it uses, our approximation framework allows for unrelated weights, thus providing the first non-trivial approximation for the problem of scheduling unrelated parallel machines with (D)oS cost functions; (3) while most of the existing approximation algorithms are based on convex programming, our approximation framework is fully combinatorial and runs in strongly polynomial time; (4) the family of (D)oS cost functions considered in the current paper is more general than the one considered in the existing literature, providing a more accurate abstraction for practical energy conservation scenarios; and (5) we obtain the first approximation ratio for GND with (D)oS cost functions that depends only on the parameters of the resources technology and does not grow with the number of resources, the number of requests, or their weights. The design of our approximation framework relies heavily on Roughgarden s smoothness toolbox (JACM 2015), thus demonstrating the possible usefulness of this toolbox in the area of approximation algorithms.
AB - In a generalized network design (GND) problem, a set of resources are assigned (non-exclusively) to multiple requests. Each request contributes its weight to the resources it uses and the total load on a resource is then translated to the cost it incurs via a resource specific cost function. Motivated by energy efficiency applications, recently, there is a growing interest in GND using cost functions that exhibit (dis)economies of scale ((D)oS), namely, cost functions that appear subadditive for small loads and superadditive for larger loads. The current paper advances the existing literature on approximation algorithms for GND problems with (D)oS cost functions in various aspects: (1) while the existing results are restricted to routing requests in undirected graphs, identifying the resources with the graph’s edges, the current paper presents a generic approximation framework that yields approximation results for a much wider family of requests (including various types of Steiner tree and Steiner forest requests) in both directed and undirected graphs, where the resources can be identified with either the edges or the vertices; (2) while the existing results assume that a request contributes the same weight to each resource it uses, our approximation framework allows for unrelated weights, thus providing the first non-trivial approximation for the problem of scheduling unrelated parallel machines with (D)oS cost functions; (3) while most of the existing approximation algorithms are based on convex programming, our approximation framework is fully combinatorial and runs in strongly polynomial time; (4) the family of (D)oS cost functions considered in the current paper is more general than the one considered in the existing literature, providing a more accurate abstraction for practical energy conservation scenarios; and (5) we obtain the first approximation ratio for GND with (D)oS cost functions that depends only on the parameters of the resources technology and does not grow with the number of resources, the number of requests, or their weights. The design of our approximation framework relies heavily on Roughgarden s smoothness toolbox (JACM 2015), thus demonstrating the possible usefulness of this toolbox in the area of approximation algorithms.
KW - (dis)economies of scale
KW - Approximation algorithms
KW - Best response dynamics
KW - Energy consumption
KW - Generalized network design
KW - Real exponent polynomial cost functions
KW - Smoothness
UR - http://www.scopus.com/inward/record.url?scp=85049912867&partnerID=8YFLogxK
U2 - https://doi.org/10.1145/3188745.3188812
DO - https://doi.org/10.1145/3188745.3188812
M3 - منشور من مؤتمر
T3 - Proceedings of the Annual ACM Symposium on Theory of Computing
SP - 902
EP - 911
BT - STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
A2 - Henzinger, Monika
A2 - Kempe, David
A2 - Diakonikolas, Ilias
T2 - 50th Annual ACM Symposium on Theory of Computing, STOC 2018
Y2 - 25 June 2018 through 29 June 2018
ER -