stable allocations and flows
play

Stable allocations and flows as Fleiner 1 Tam Summer School on - PowerPoint PPT Presentation

Sep 24, 2022 •277 likes •1.04k views

Stable allocations and flows as Fleiner 1 Tam Summer School on Matching Problems, Markets, and Mechanisms 26 June 2013, Budapest 1 Budapest University of Technology and Economics Stable matchings Model: Stable matchings Model: Boys

  1. Stable allocations and flows as Fleiner 1 Tam´ Summer School on Matching Problems, Markets, and Mechanisms 26 June 2013, Budapest 1 Budapest University of Technology and Economics

  2. Stable matchings Model:

  3. Stable matchings Model: Boys

  4. Stable matchings Model: Boys and girls

  5. Stable matchings Model: Boys and girls with possible marriages are given.

  6. Stable matchings Model: Boys and girls with possible marriages are given. Marriage scheme: matching .

  7. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners.

  8. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges .

  9. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges .

  10. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists.

  11. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one:

  12. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one:

  13. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners,

  14. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance.

  15. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate:

  16. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose

  17. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly.

  18. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly.

  19. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly.

  20. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly.

  21. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly. When no boy proposes

  22. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly. When no boy proposes then we got a stable matching .

  23. Stable matchings 1 3 2 1 2 1 2 1 2 1 3 2 2 2 1 1 1 3 1 2 3 4 1 5 4 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 Model: Boys and girls with possible marriages are given. Marriage scheme: matching . Preferences on possible partners. Instability may occur along blocking edges . A matching is stable if no blocking edge exists. The proposal algorithm of Gale and Shapley always finds one: Boys propose to best partners, girls reject boys with no chance. We iterate: rejected boys propose and girls reject alternatingly. When no boy proposes then we got a stable matching . Man-optimality: each boy gets the best stable partner.

  24. Stable allocations and properties Extension of the model: capacities for vxs and edges (partnerships).

  25. Stable allocations and properties 2 3 1 3 2 1 2 2 1 2 1 2 1 3 2 2 2 2 2 1 1 1 3 1 2 3 4 1 2 5 4 2 3 2 2 4 1 3 3 3 5 1 3 1 2 1 2 1 2 1 2 3 2 2 Extension of the model: capacities for vxs and edges (partnerships).

  26. Stable allocations and properties 2 3 1 1 3 2 1 2 2 1 2 1 2 1 3 2 2 1 1 1 / 3 2 2 2 2 1 1 1 3 1 2 3 4 1 2 5 4 2 3 2 2 4 1 1 / 3 3 3 3 5 1 / 3 1 1 3 1 2 1 2 1 1 2 1 2 3 2 2 Extension of the model: capacities for vxs and edges (partnerships). An allocation an assignment of intensities to edges st capacities of edges and vxs are observed.

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

A stable scheme for simulation of incompressible flows in time-dependent domains and hemodynamic

A stable scheme for simulation of incompressible flows in time-dependent domains and hemodynamic

A stable scheme for simulation of incompressible flows in time-dependent domains and hemodynamic applications Yuri Vassilevski 1 , 2 , 3 Maxim Olshanskii 4 Alexander Danilov 1 , 2 , 3 Alexander Lozovskiy 1 Victoria Salamatova 1 , 2 , 3 1 Marchuk

1.21k views • 59 slides
KE and entropy stable schemes for compressible flows Praveen. C praveen@math.tifrbng.res.in

KE and entropy stable schemes for compressible flows Praveen. C praveen@math.tifrbng.res.in

KE and entropy stable schemes for compressible flows Praveen. C praveen@math.tifrbng.res.in Tata Institute of Fundamental Research Center for Applicable Mathematics Bangalore 560065 http://math.tifrbng.res.in/ praveen Indo-German Conference

520 views • 39 slides
The Theory and Practice of Market Design (work in progress) Nobel Lecture December 8, 2012

The Theory and Practice of Market Design (work in progress) Nobel Lecture December 8, 2012

The Theory and Practice of Market Design (work in progress) Nobel Lecture December 8, 2012 The theory of stable allocations and the practice of market design Plan of talk: How stable allocations and matching mechanisms connect to

584 views • 34 slides
Entropy stable schemes for compressible flows on unstructured meshes Deep Ray Tata Institute of

Entropy stable schemes for compressible flows on unstructured meshes Deep Ray Tata Institute of

Entropy stable schemes for compressible flows on unstructured meshes Deep Ray Tata Institute of Fundamental Research Center for Applicable Mathematics Bangalore deep@math.tifrbng.res.in http://math.tifrbng.res.in/deep SCPDE-2014, Hong Kong

690 views • 52 slides
INVESTOR PRESENTATION A PRIL 13, 2018 STABLE CASH FLOWS ANCHORED BY RECURRING INCOME AND REVENUE

INVESTOR PRESENTATION A PRIL 13, 2018 STABLE CASH FLOWS ANCHORED BY RECURRING INCOME AND REVENUE

INVESTOR PRESENTATION A PRIL 13, 2018 STABLE CASH FLOWS ANCHORED BY RECURRING INCOME AND REVENUE RLC s investment portfolio CY 2017 Investment portfolio posted: continues to account for a +7% in Revenues major share in Revenues,

453 views • 18 slides
1 Project Cash Flows Project cash flows for a capital investment typically fall into one of

1 Project Cash Flows Project cash flows for a capital investment typically fall into one of

Analyzing Project Cash Flows Chapter 12 1 Principles Applied in This Chapter Principle 3: Cash Flows Are the Source of Value. Principle 5: Individuals Respond to Incentives. 2 Learning Objectives Identify incremental cash flows that

570 views • 19 slides
IoT-Flows: Lightweight Policy Enforcement of Information Flows in IoT Infrastructures Jos

IoT-Flows: Lightweight Policy Enforcement of Information Flows in IoT Infrastructures Jos

IoT-Flows: Lightweight Policy Enforcement of Information Flows in IoT Infrastructures Jos Augusto Suruagy Monteiro Centro de Informtica - UFPE IoT-Flows: US Subteam (PIs) Prof. Atul Prakash (UMich) Expert on security and IoT Prof. Darko

455 views • 24 slides
IRC Sect. 704(b): Allocations to Partners Navigating Complex Rules on Determining Validity of

IRC Sect. 704(b): Allocations to Partners Navigating Complex Rules on Determining Validity of

Presenting a live 110-minute teleconference with interactive Q&A IRC Sect. 704(b): Allocations to Partners Navigating Complex Rules on Determining Validity of Partnership Allocations WEDNESDAY, DECEMBER 12, 2012 1pm Eastern | 12pm

1k views • 89 slides
IRC Sect. 704(b): Allocations to Partners Navigating Complex Rules on Determining Validity of

IRC Sect. 704(b): Allocations to Partners Navigating Complex Rules on Determining Validity of

Presenting a live 110 minute teleconference with interactive Q&A IRC Sect. 704(b): Allocations to Partners Navigating Complex Rules on Determining Validity of Partnership Allocations TUES DAY, JANUARY 10, 2012 1pm Eastern | 12pm

1.16k views • 100 slides
A large deviation approach to computing rare transitions in multi-stable stochastic turbulent

A large deviation approach to computing rare transitions in multi-stable stochastic turbulent

A large deviation approach to computing rare transitions in multi-stable stochastic turbulent flows Jason Laurie and Freddy Bouchet Laboratoire de Physique, ENS de Lyon, France ENS de Lyon, 13 June 2012 Bistability in Rotating Tank Experiment

224 views • 20 slides
Numerical Modelling of Granular Flows B. Maury Laboratoire de Math ematiques, Universit e

Numerical Modelling of Granular Flows B. Maury Laboratoire de Math ematiques, Universit e

Numerical Modelling of Granular Flows B. Maury Laboratoire de Math ematiques, Universit e Paris-Sud, Orsay Model (hard spheres, non elastic collisions) Strategies A stable method to handle non elastic collisions Numerical tests

1.09k views • 81 slides
Protection of flows Protection of flows under targeted attacks under targeted attacks Jannik

Protection of flows Protection of flows under targeted attacks under targeted attacks Jannik

Protection of flows Protection of flows under targeted attacks under targeted attacks Jannik Matuschke Tom McCormick Gianpaolo Oriolo TU Berlin UBC Vancouver Tor Vergata Britta Peis Martin Skutella RWTH Aachen TU Berlin Robust flows

531 views • 28 slides
OpenStack Stable What it actually means to maintain stable branches Matthew Treinish (irc:

OpenStack Stable What it actually means to maintain stable branches Matthew Treinish (irc:

OpenStack Stable What it actually means to maintain stable branches Matthew Treinish (irc: mtreinish) Matt Riedemann (irc: mriedem) Ihar Hrachyshka (irc: ihrachys) Newton Summit, Austin, TX - 2016/04/25 Agenda Introductions Who cares?

664 views • 27 slides
Toda flows, gradient flows and the generalized Flaschka map Anthony Bloch Dissipation and

Toda flows, gradient flows and the generalized Flaschka map Anthony Bloch Dissipation and

1 Toda flows, gradient flows and the generalized Flaschka map Anthony Bloch Dissipation and Radiation Induced Instability Toda and gradient flows, metric and metriplectic flows The Pukhanzky condition Generalized Flaschka Map

1.02k views • 54 slides
Global FDI flows were down by 7% in 2014 compared to 2013 GLOBAL FOREIGN DIRECT INVESTMENT FLOWS,

Global FDI flows were down by 7% in 2014 compared to 2013 GLOBAL FOREIGN DIRECT INVESTMENT FLOWS,

Themes of the report Overview of FDI in the world and in Latin America Special analysis of FDI in the Caribbean subregion Transnational firms and the environment Conclusions and outlook for 2015 Global FDI flows were down by 7%

435 views • 27 slides
RE-ZONING YOUR LIBRARY THROUGH DATA-DRIVEN SPACE ALLOCATIONS RE-ZONING YOUR LIBRARY THROUGH

RE-ZONING YOUR LIBRARY THROUGH DATA-DRIVEN SPACE ALLOCATIONS RE-ZONING YOUR LIBRARY THROUGH

RE-ZONING YOUR LIBRARY THROUGH DATA-DRIVEN SPACE ALLOCATIONS RE-ZONING YOUR LIBRARY THROUGH DATA-DRIVEN SPACE ALLOCATIONS Southeastern Library Assessment Conference November 2015 Robert E. Fox, Jr. Bruce L. Keisling Dean, University

674 views • 31 slides
7/24/2016 Plasma (Cell) Membrane Cell membrane separates living cell from nonliving surroundings

7/24/2016 Plasma (Cell) Membrane Cell membrane separates living cell from nonliving surroundings

7/24/2016 Plasma (Cell) Membrane Cell membrane separates living cell from nonliving surroundings thin barrier = 8nm thick controls traffic in & out of the cell selectively permeable Chapter 7 allows some substances to cross

473 views • 7 slides
Methodology for Computer Science Research Lecture 4: Mathematical Modeling Andrey Lukyanenko

Methodology for Computer Science Research Lecture 4: Mathematical Modeling Andrey Lukyanenko

Methodology for Computer Science Research Lecture 4: Mathematical Modeling Andrey Lukyanenko Department of Computer Science and Engineering Aalto University, School of Science and Technology andrey.lukyanenko@tkk.fi October 6, 2011

696 views • 42 slides
Analysis and simulation of a two phase flow F. Sma , A. Bourgeat, M. Jurak model with phase

Analysis and simulation of a two phase flow F. Sma , A. Bourgeat, M. Jurak model with phase

Scaling Up and Modeling for Transport and Flow in Porous Media Analysis and simulation of a two Dubrovnik, Croatia, 13-16 October 2008 phase flow model with phase appari- tion/disappearance Analysis and simulation of a two phase flow F.

885 views • 88 slides
Sum-free sets and shift automorphisms Peter J. Cameron p.j.cameron@qmul.ac.uk Workshop on Graphs

Sum-free sets and shift automorphisms Peter J. Cameron p.j.cameron@qmul.ac.uk Workshop on Graphs

Sum-free sets and shift automorphisms Peter J. Cameron p.j.cameron@qmul.ac.uk Workshop on Graphs and Asynchronous Systems, 20 May 2008 Cayley graphs Theorem 1. There is a countable graph R such that, if a random graph X on a fixed countable

1.19k views • 5 slides
Gestational This webcast is made possible by the support of the Colorado Diabetes Prevention and

Gestational This webcast is made possible by the support of the Colorado Diabetes Prevention and

Acknow ledgm ents Gestational This webcast is made possible by the support of the Colorado Diabetes Prevention and Control Program (CDPCP), which is working to improve access to quality care for women with Gestational Diabetes in Colorado.

384 views • 10 slides
7 FEM Modeling: Introduction IFEM Ch 7 Slide 1 Department of Engineering Mechanics PhD.

7 FEM Modeling: Introduction IFEM Ch 7 Slide 1 Department of Engineering Mechanics PhD.

Department of Engineering Mechanics PhD. TRUONG Tich Thien Introduction to FEM 7 FEM Modeling: Introduction IFEM Ch 7 Slide 1 Department of Engineering Mechanics PhD. TRUONG Tich Thien Introduction to FEM FEM Terminology degrees of

438 views • 26 slides
Monetary Policy Report July 2018 Chapter 1 Figure 1.1. Repo rate with uncertainty bands Per

Monetary Policy Report July 2018 Chapter 1 Figure 1.1. Repo rate with uncertainty bands Per

Monetary Policy Report July 2018 Chapter 1 Figure 1.1. Repo rate with uncertainty bands Per cent Note. The uncertainty bands for the repo rate are based on the Riksbanks historical forecasting errors and Source: The Riksbank the ability

900 views • 64 slides
REFINEMENT OF THE PION PDF IMPLEMENTING DRELL- YAN EXPERIMENTAL DATA Patrick B Barry 1 , Nobuo

REFINEMENT OF THE PION PDF IMPLEMENTING DRELL- YAN EXPERIMENTAL DATA Patrick B Barry 1 , Nobuo

REFINEMENT OF THE PION PDF IMPLEMENTING DRELL- YAN EXPERIMENTAL DATA Patrick B Barry 1 , Nobuo Sato 2 , W. Melnitchouk 3 , Chueng-Ryong Ji 1 pcbarry@ncsu.e .edu North Carolina State University 1 University of Connecticut 2 Thomas Jefferson

561 views • 29 slides

More recommend