BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20200101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210506T100000
DTEND;TZID=Asia/Seoul:20210506T110000
DTSTAMP:20260420T111504
CREATED:20210319T045807Z
LAST-MODIFIED:20240705T190027Z
UID:3813-1620295200-1620298800@dimag.ibs.re.kr
SUMMARY:Raul Lopes\, Adapting the Directed Grid Theorem into an FPT Algorithm
DESCRIPTION:The Grid Theorem of Robertson and Seymour [JCTB\, 1986] is one of the most important tools in the field of structural graph theory\, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem in digraphs was conjectured by Johnson et al. [JCTB\, 2001] \, and proved by Kawarabayashi and Kreutzer [STOC\, 2015]. They showed that there is a function f(k) such that every digraph of directed tree-width at least f(k) contains a cylindrical grid of order k as a butterfly minor and stated that their proof can be turned into an XP algorithm\, with parameter k\, that either constructs a decomposition of the appropriate width\, or finds the claimed large cylindrical grid as a butterfly minor. \nIn this talk\, we present the ideas used in our adaptation of the Directed Grid Theorem into an FPT algorithm. We provide two FPT algorithms with parameter k. The first one either produces an arboreal decomposition of width 3k-2 or finds a haven of order k in a digraph D. The second one uses a bramble B that naturally occurs in digraphs of large directed tree-width to find a well-linked set of order k that is contained in the set of vertices of a path hitting all elements of B. As tools to prove these results\, we show how to solve a generalized version of the problem of finding balanced separators for a given set of vertices T in FPT time with parameter |T|. \nJoint work with Victor Campos\, Ana Karolinna Maia\, and Ignasi Sau.
URL:https://dimag.ibs.re.kr/event/2021-05-06/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
END:VCALENDAR