Reverse 2-median problem on trees

Upgrading p-median problem is a problem of finding the best median of the given graph through modification of its parameters. The current paper develops a polynomial-time model to address this problem when the weights of vertices can be varying under a given budget. Moreover, in the case where the considering graph has a special structure, namely a path, a linear time algorithm will be proposed for solving the problem with uniform cost.

show abstract

“…Proof : If x is in form I, then it is easy to see that it is also an admissible optimal solution in form I for LP k+1 according to (3 …”

Section: Lemma 34 a Suppose X Is An Admissible Solution In Form I Wimentioning

confidence: 99%

“…In [2], Burkard et al proved reverse 1-median problem with variable edge lengths is N P-hard. They consider reverse 1-median problem with a unit cost function on cycle graphs [2] and reverse 2-median problem [3].…”

mentioning

confidence: 99%

Upgrading p-Median Problem on a Path

Sepasian

Rahbarnia

2014

J Math Model Algor

View full text Add to dashboard Cite

show abstract

“…On the other hand, Burkard, Gassner and Hatzl [2] proved that the reverse 1-median problem is N P-hard on general graphs but can be solved in linear time on a cycle. In [3] the same authors suggest an O(n log n) time algorithm for the reverse 2-median problem on trees and the reverse 1-median problem on unicycle graphs.…”

Section: Inverse and Reverse Location Problemsmentioning

confidence: 99%

“…If we want to decrease the optimality gap by δ, the weight change δ s of point P s and δ t of point P t have to fulfill according to (3) and (4):…”

Section: A Greedy Algorithm For the Inverse Fermat-weber Problem Withmentioning

confidence: 99%

The inverse Fermat–Weber problem

Burkard

Galavii

Gassner

2010

European Journal of Operational Research

Self Cite

View full text Add to dashboard Cite

“…A variety of inverse combinatorial optimization problems have been studied during the last two decades. Main reference includes the following: Orlin, 2000, 2001;Burkard et al, 2008;Burton and Toint 1992;Demange, 2008, 2012;Heuberger, 2004). The inverse number problems have been studied for some NP-hard optimization problems such as the maximum independent set problem ) and the minimum graph coloring problem (Chung et al, , 2010.…”

Section: Introductionmentioning

confidence: 99%

Inverse Bin-packing Number Problems: NP-Hardness and Approximation Algorithms

Chung

2012

Management Science and Financial Engineering

View full text Add to dashboard Cite

In the bin-packing problem, we deal with how to pack the items by using a minimum number of bins. In the inverse bin-packing number problem, IBPN for short, we are given a list of items and a fixed number of bins. The objective is to perturb at the minimum cost the item-size vector so that all items can be packed into the prescribed number of bins. We show that IBPN is NP-hard and provide an approximation algorithm. We also consider a variant of IBPN where the prescribed solution value should be returned by a pre-selected specific approximation algorithm.

show abstract

Reverse 2-median problem on trees

Cited by 27 publications

References 16 publications

Upgrading p-Median Problem on a Path

Upgrading p-Median Problem on a Path

The inverse Fermat–Weber problem

Inverse Bin-packing Number Problems: NP-Hardness and Approximation Algorithms

Contact Info

Product

Resources

About