TY - JOUR

T1 - Resource allocation in rooted trees subject to sum constraints and nonlinear cost functions

AU - Halman, Nir

AU - Wimer, Shmuel

N1 - Publisher Copyright:
© 2021

PY - 2021/9

Y1 - 2021/9

N2 - We study resource allocation problems in rooted trees in which demand values are given in the leaves. Single-type resources (weights) are to be assigned in the tree nodes such that the total weight in the rooted path from each leaf to the root equals its demand. The goal is to minimize the total costs of the allocated resources. It is known that the linear cost case, i.e., when the cost of a resource is proportional to its weight, is solvable in linear time. In this paper we show that when costs are monotone nondecreasing functions, which reflect, e.g., (dis)economies of scale, the problem becomes intractable, and design for it a fully polynomial time approximation scheme by formulating it as a dynamic program and using the technique of K-approximation sets and functions.

AB - We study resource allocation problems in rooted trees in which demand values are given in the leaves. Single-type resources (weights) are to be assigned in the tree nodes such that the total weight in the rooted path from each leaf to the root equals its demand. The goal is to minimize the total costs of the allocated resources. It is known that the linear cost case, i.e., when the cost of a resource is proportional to its weight, is solvable in linear time. In this paper we show that when costs are monotone nondecreasing functions, which reflect, e.g., (dis)economies of scale, the problem becomes intractable, and design for it a fully polynomial time approximation scheme by formulating it as a dynamic program and using the technique of K-approximation sets and functions.

KW - Design of algorithms

KW - Dynamic programming

KW - FPTAS

KW - K-approximation sets and functions

KW - Resource allocation

UR - http://www.scopus.com/inward/record.url?scp=85104059725&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2021.106114

DO - 10.1016/j.ipl.2021.106114

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AN - SCOPUS:85104059725

SN - 0020-0190

VL - 170

JO - Information Processing Letters

JF - Information Processing Letters

M1 - 106114

ER -