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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210907T163000
DTEND;TZID=Asia/Seoul:20210907T173000
DTSTAMP:20221209T144600
CREATED:20210907T073000Z
LAST-MODIFIED:20210901T010222Z
UID:4495-1631032200-1631035800@dimag.ibs.re.kr
SUMMARY:Dabeen Lee (이다빈)\, Mixing sets\, submodularity\, and chance-constrained optimization
DESCRIPTION:A particularly important substructure in modeling joint linear chance-constrained programs with random right-hand sides and finite sample space is the intersection of mixing sets with common binary variables (and possibly a knapsack constraint). In this talk\, we first explain basic mixing sets by establishing a strong and previously unrecognized connection to submodularity. In particular\, we show that mixing inequalities with binary variables are nothing but the polymatroid inequalities associated with a specific submodular function. This submodularity viewpoint enables us to unify and extend existing results on valid inequalities and convex hulls of the intersection of multiple mixing sets with common binary variables. Then\, we study such intersections under an additional linking constraint lower bounding a linear function of the continuous variables. This is motivated from the desire to exploit the information encoded in the knapsack constraint arising in joint linear CCPs via the quantile cuts. We propose a new class of valid inequalities and characterize when this new class along with the mixing inequalities are sufficient to describe the convex hull. This is based on joint work with Fatma Fatma Kılınç-Karzan and Simge Küçükyavuz.
URL:https://dimag.ibs.re.kr/event/2021-09-07/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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DTSTART;TZID=Asia/Seoul:20210928T163000
DTEND;TZID=Asia/Seoul:20210928T173000
DTSTAMP:20221209T144600
CREATED:20210928T073000Z
LAST-MODIFIED:20210831T095827Z
UID:4452-1632846600-1632850200@dimag.ibs.re.kr
SUMMARY:Kevin Hendrey\, Extremal functions for sparse minors
DESCRIPTION:The extremal function $c(H)$ of a graph $H$ is the supremum of densities of graphs not containing $H$ as a minor\, where the density of a graph is the ratio of the number of edges to the number of vertices. Myers and Thomason (2005)\, Norin\, Reed\, Thomason and Wood (2020)\, and Thomason and Wales (2019) determined the asymptotic behaviour of $c(H)$ for all polynomially dense graphs $H$\, as well as almost all graphs of constant density. We explore the asymptotic behavior of the extremal function in the regime not covered by the above results\, where in addition to having constant density the graph $H$ is in a graph class admitting strongly sublinear separators. We establish asymptotically tight bounds in many cases. For example\, we prove that for every planar graph $H$\, \[c(H) = (1+o(1))\max (v(H)/2\, v(H)-\alpha(H))\,\] extending recent results of Haslegrave\, Kim and Liu (2020). Joint work with Sergey Norin and David R. Wood.
URL:https://dimag.ibs.re.kr/event/2021-09-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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