Node-Balancing by Edge-Increments

Friedrich Eisenbrand; Shay Moran; Rom Pinchasi; Martin Skutella

doi:10.1007/978-3-662-48350-3_38

Node-Balancing by Edge-Increments

Friedrich Eisenbrand, Shay Moran, Rom Pinchasi, Martin Skutella

Mathematics

Technion - Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Suppose you are given a graph G = (V,E) with a weight assignment w : V → Z and that your objective is to modify w using legal steps such that all vertices will have the same weight, where in each legal step you are allowed to choose an edge and increment the weights of its end points by 1. In this paper we study several variants of this problem for graphs and hypergraphs. On the combinatorial side we show connections with fundamental results from matching theory such as Hall’s Theorem and Tutte’s Theorem. On the algorithmic side we study the computational complexity of associated decision problems. Our main results are a characterization of the graphs for which any initial assignment can be balanced by edge-increments and a strongly polynomial-time algorithm that computes a balancing sequence of increments if one exists.

Original language	English
Title of host publication	Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
Editors	Nikhil Bansal, Irene Finocchi
Pages	450-458
Number of pages	9
DOIs	https://doi.org/10.1007/978-3-662-48350-3_38
State	Published - 2015
Event	23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9294

Conference

Conference	23rd European Symposium on Algorithms, ESA 2015
Country/Territory	Greece
City	Patras
Period	14/09/15 → 16/09/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-48350-3_38

Cite this

Eisenbrand, F., Moran, S., Pinchasi, R., & Skutella, M. (2015). Node-Balancing by Edge-Increments. In N. Bansal, & I. Finocchi (Eds.), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings (pp. 450-458). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294). https://doi.org/10.1007/978-3-662-48350-3_38

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title = "Node-Balancing by Edge-Increments",

abstract = "Suppose you are given a graph G = (V,E) with a weight assignment w : V → Z and that your objective is to modify w using legal steps such that all vertices will have the same weight, where in each legal step you are allowed to choose an edge and increment the weights of its end points by 1. In this paper we study several variants of this problem for graphs and hypergraphs. On the combinatorial side we show connections with fundamental results from matching theory such as Hall{\textquoteright}s Theorem and Tutte{\textquoteright}s Theorem. On the algorithmic side we study the computational complexity of associated decision problems. Our main results are a characterization of the graphs for which any initial assignment can be balanced by edge-increments and a strongly polynomial-time algorithm that computes a balancing sequence of increments if one exists.",

author = "Friedrich Eisenbrand and Shay Moran and Rom Pinchasi and Martin Skutella",

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Eisenbrand, F, Moran, S , Pinchasi, R & Skutella, M 2015, Node-Balancing by Edge-Increments. in N Bansal & I Finocchi (eds), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9294, pp. 450-458, 23rd European Symposium on Algorithms, ESA 2015, Patras, Greece, 14/09/15. https://doi.org/10.1007/978-3-662-48350-3_38

Node-Balancing by Edge-Increments. / Eisenbrand, Friedrich; Moran, Shay ; Pinchasi, Rom et al.
Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. ed. / Nikhil Bansal; Irene Finocchi. 2015. p. 450-458 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Suppose you are given a graph G = (V,E) with a weight assignment w : V → Z and that your objective is to modify w using legal steps such that all vertices will have the same weight, where in each legal step you are allowed to choose an edge and increment the weights of its end points by 1. In this paper we study several variants of this problem for graphs and hypergraphs. On the combinatorial side we show connections with fundamental results from matching theory such as Hall’s Theorem and Tutte’s Theorem. On the algorithmic side we study the computational complexity of associated decision problems. Our main results are a characterization of the graphs for which any initial assignment can be balanced by edge-increments and a strongly polynomial-time algorithm that computes a balancing sequence of increments if one exists.

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Eisenbrand F, Moran S , Pinchasi R, Skutella M. Node-Balancing by Edge-Increments. In Bansal N, Finocchi I, editors, Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. 2015. p. 450-458. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-48350-3_38

Node-Balancing by Edge-Increments

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