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X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETTO:+0900
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DTSTART:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260106T163000
DTEND;TZID=Asia/Seoul:20260106T173000
DTSTAMP:20260416T054751
CREATED:20251030T130957Z
LAST-MODIFIED:20251226T132814Z
UID:11793-1767717000-1767720600@dimag.ibs.re.kr
SUMMARY:Daniel Mock\, A Simple Algorithm for the Dominating Set Problem and More
DESCRIPTION:In [1]\, Fabianski et. al. developed a simple\, yet surprisingly powerful algorithmic framework to develop efficient parameterized graph algorithms. Notably they derive a simple parameterized algorithm for the dominating set problem on a variety of graph classes\, including powers of nowhere dense classes and biclique-free classes. These results encompass a wide range of previously known results and often improve the best known running times. Similar results follow for the distance-r variation of dominating set and for independent set. The running time of the algorithm is closely tied to model-theoretic properties\, i.e. stability and the Helly property. \nWe build upon these results and develop a similar algorithm which only relies on the strong Helly property and does not need stability. For the dominating set problem\, we get a parameterized algorithm that works (additionally to biclique-free classes and powers of nowhere dense classes) weakly gamma-closed classes while being simpler and faster than previously known results. \nIn this talk\, we introduce the basic framework\, results by Fabianski et. al and connections to other areas. We discuss our new insights and possible research directions. \n[1] Grzegorz Fabianski\, Michal Pilipczuk\, Sebastian Siebertz\, Szymon Torunczyk: Progressive Algorithms for Domination and Independence. STACS 2019
URL:https://dimag.ibs.re.kr/event/2026-01-06/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260113T163000
DTEND;TZID=Asia/Seoul:20260113T173000
DTSTAMP:20260416T054751
CREATED:20251201T074437Z
LAST-MODIFIED:20251208T125825Z
UID:11942-1768321800-1768325400@dimag.ibs.re.kr
SUMMARY:Ferdinand Ihringer\, Boolean Functions Analysis in the Grassmann Graph
DESCRIPTION:Boolean function analysis for the hypercube $\{ 0\, 1 \}^n$ is a well-developed field and has many famous results such as the FKN Theorem or Nisan-Szegedy Theorem. One easy example is the classification of Boolean degree $1$ functions: If $f$ is a real\, $n$-variate affine function which is Boolean on the $n$-dimensional hypercube (that is\, $f(x) \in \{ 0\, 1 \}$ for $x \in \{ 0\, 1 \}^n$)\, then $f(x) = 0$\, $f(x) = 1$\, $f(x) = x_i$ or $f(x) = 1 – x_i$. The same classification (essentially) holds if we restrict $\{ 0\, 1\}^n$ to elements with Hamming weight $k$ if $n-k\, k \geq 2$. If we replace $k$-sets of $\{ 1\, \ldots\, n \}$ by $k$-spaces in $V(n\, q)$\, the $n$-dimensional vector space over the field with $q$ elements\, then suddenly even the simple question of classifying Boolean degree $1$ functions\, here traditionally known as Cameron-Liebler classes\, becomes seemingly hard to solve. \nWe will discuss some results on low-degree Boolean functions in the vector space setting. Most notably\, we will discuss how vector space Ramsey numbers\, so extremal combinatorics\, can be utilized in this finite geometrical setting.
URL:https://dimag.ibs.re.kr/event/2026-01-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260120T163000
DTEND;TZID=Asia/Seoul:20260120T173000
DTSTAMP:20260416T054751
CREATED:20251012T113928Z
LAST-MODIFIED:20251212T235119Z
UID:11717-1768926600-1768930200@dimag.ibs.re.kr
SUMMARY:Tomáš Masařík\, Separator Theorem for Minor-free Graphs in Linear Time
DESCRIPTION:The planar separator theorem by Lipton and Tarjan [FOCS ’77\, SIAM Journal on Applied Mathematics ’79] states that any planar graph with $n$ vertices has a balanced separator of size $O(\sqrt{n})$ that can be found in linear time. This landmark result kicked off decades of research on designing linear or nearly linear-time algorithms on planar graphs. In an attempt to generalize Lipton-Tarjan’s theorem to nonplanar graphs\, Alon\, Seymour\, and Thomas [STOC ’90\, Journal of the AMS ’90] showed that any minor-free graph admits a balanced separator of size $O(\sqrt{n})$ that can be found in $O(n^{3/2})$ time. The superlinear running time in their separator theorem is a key bottleneck for generalizing algorithmic results from planar to minor-free graphs. Despite extensive research for more than two decades\, finding a balanced separator of size $O(\sqrt{n})$ in (linear) $O(n)$ time for minor-free graphs remains a major open problem. Known algorithms either give a separator of size much larger than $O(\sqrt{n})$ or have superlinear running time\, or both. \nIn this paper\, we answer the open problem affirmatively. Our algorithm is very simple: it runs a vertex-weighted variant of breadth-first search (BFS) a constant number of times on the input graph. Our key technical contribution is a weighting scheme on the vertices to guide the search for a balanced separator\, offering a new connection between the size of a balanced separator and the existence of a clique-minor model. We believe that our weighting scheme may be of independent interest. \nThis is a joint work with Édouard Bonnet\, Tuukka Korhonen\, Hung Le\, and Jason Li.
URL:https://dimag.ibs.re.kr/event/2026-01-20/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260127T163000
DTEND;TZID=Asia/Seoul:20260127T173000
DTSTAMP:20260416T054751
CREATED:20251015T110913Z
LAST-MODIFIED:20260106T021752Z
UID:11724-1769531400-1769535000@dimag.ibs.re.kr
SUMMARY:Daniel Dadush\, A Strongly Polynomial Algorithm for Linear Programs with at Most Two Non-Zero Entries per Row or Column
DESCRIPTION:We give a strongly polynomial algorithm for minimum cost generalized flow\, and hence for optimizing any linear program with at most two non-zero entries per row\, or at most two non-zero entries per column. Primal and dual feasibility were shown by Végh (MOR ’17) and Megiddo (SICOMP ’83) respectively. Our result can be viewed as progress towards understanding whether all linear programs can be solved in strongly polynomial time\, also referred to as Smale’s 9th problem. Our approach is based on the recent primal-dual interior point method (IPM) due to Allamigeon\, Dadush\, Loho\, Natura and Végh (FOCS ’22). The number of iterations needed by the IPM is bounded\, up to a polynomial factor in the number of inequalities\, by the straight line complexity of the central path. Roughly speaking\, this is the minimum number of pieces of any piecewise linear curve that multiplicatively approximates the central path. As our main contribution\, we show that the straight line complexity of any minimum cost generalized flow instance is polynomial in the number of arcs and vertices. By applying a reduction of Hochbaum (ORL ’04)\, the same bound applies to any linear program with at most two non-zeros per column or per row \nJoint work with Zhuan Khye Koh (Boston U)\, Bento Natura (Columbia)\, Neil Olver (LSE)\, and László A. Végh (Bonn).
URL:https://dimag.ibs.re.kr/event/2026-01-27/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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