HOUSING MARKETS: graphs & co.

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Presentation transcript:

HOUSING MARKETS: graphs & co. Katarína Cechlárová P. J. Šafárik University, Košice, Slovakia Bilbao, October 23, 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015 Top Trading Cycles algorithm Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015 Graphs – Who is who 1 Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

TTC algorithm for strict preferences Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

TTC algorithm for strict preferences Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

TTC algorithm for our example Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

TTC algorithm for our example Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015 Graphs – Who is who 2 Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Algorithm to find strong core Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Computational complexity – Who is Who Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Brief history: economic equilibrium Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015 p1 > p2 Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Approximate equilibrium Definition. Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Approximate equilibrium Definition. Theorem (KC & Schlotter 2010). Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015 Theorem (KC & Jelínková 2011). Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Motivation in the movie Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Housing market with divorcing and engaged pairs Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Each divorcing couple needs an egaged pair Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015 1 sK 2 Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

The talk was based on papers: K. Cechlárová, T. Fleiner, Housing markets through graphs, Algorithmica 58/1, 170-187, 2010. K. Cechlárová, E. Jelínková, An efficient implementation of the equilibrium algorithm for housing markets with duplicate houses, Information Processing Letters, 111/ 13, 667-670 (2011). K. Cechlárová, I. Schlotter, Computing the Deficiency of Housing Markets with Duplicate Houses, LNCS 6478, Parameterized and Exact Computation, 72-83 (2010) K. Cechlárová, E. Jelínková, Approximability of Economic Equilibrium for Housing Markets With Duplicate Houses, WG2011, LNCS 6986, eds. P. Kolman a J. Kratochvíl, 95-106 (2011) K. Cechlárová, T. Fleiner , Zs. Janko, House-swapping with divorcing and engaged pairs, Preprint UMV UPJŠ, 2015. Katarína Cechlárová Housing markets: graphs & co. Bilbao 2015

Thank you for your attention!