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IGAFIT Algorithmic Colloquium #6
December 10, 2020 
Circulation Control for Faster Minimum Cost Flow in UnitCapacity Graphs 
Adrian Vladu, Université de Paris 
In recent years, continuous optimization primitives have become an essential component in the algorithmist’s toolkit. Among other developments, this has led to tremendous progress on the quest for developing fast graph algorithms. In this talk I will give an overview of the techniques based on interior point methods, which have been instrumental to obtaining a set of faster algorithms for fundamental graph problems, which include an m^{4/3+o(1)} log W time algorithm for solving the minimum cost flow problem in graphs with unit capacity. For sparse graphs, our algorithm improves over the best known running time for this problem and, by wellknown reductions, also implies improved running times for the shortest path problem with negative weights, minimum cost bipartite bmatching when b_{1} = O(m), and recovers the running time of the recent unit capacity maximum flow algorithm due to LiuSidford. Based on https://arxiv.org/abs/2003.04863 
IGAFIT Algorithmic Colloquium #5
November 26, 2020 
Fully Online Matching 
Zhiyi Huang, University of Hong Kong 
Motivated by applications such as ride sharing, we introduce a fully online model of maximum cardinality matching in which all vertices arrive and depart online. On the arrival of a vertex, its edges to previouslyarrived vertices are revealed. The vertex can be matched anytime before its departure, which is after all its neighbors’ arrivals. This fully online matching model generalizes the online bipartite matching model which only considers bipartite graphs and assumes one side of the vertices to be offline. We generalize the Ranking and WaterFilling algorithms to fully online matching and its fractional relaxation respectively. The former is 0.521competitive in general graphs, and 0.567competitive in bipartite graphs, and the latter is 0.585 competitive in both cases. Further, we prove that fully online matching is strictly harder than online bipartite matching, because no online algorithm can be 0.6317 <(11/e)competitive in fully online matching even for bipartite graphs. Finally, we introduce new algorithms that are strictly better than Ranking and WaterFilling in fully online matching. 
see the video: Colloquium #5 
IGAFIT Algorithmic Colloquium #4
November 12, 2020 
New Lower and Upper Bounds for quantile summary algorithms 
Graham Cormode, University of Warwick 
Finding the median, or more generally quantiles, is a core problem in data analysis. The question has been heavily studied in streaming and related models of computation, for over four decades. In this talk I will present some recent advances:

IGAFIT Algorithmic Colloquium #3
October 29, 2020 
A (Slightly) Improved Approximation Algorithm for Metric TSP 
Nathan Klein, University of Washington 
In this talk, he describes recent work in which he obtains a 3/2ε approximation algorithm for metric TSP, for some ε>10^{36}. This slightly improves over the classical 3/2 approximation algorithm due to Christofides [1976] and Serdyukov [1978]. The talk focuses on giving an overview of the key ideas involved. This is joint work with Anna Karlin and Shayan Oveis Gharan. 
IGAFIT Algorithmic Colloquium #2
October 15, 2020 
An almostlinear time deterministic algorithm for expander decomposition 
Thatchaphol Saranurak, Toyota Technological Institute at Chicago 
Expander decomposition is a powerful tool in many areas on graph algorithms (e.g. approximation algorithm, dynamic algorithm, distributed algorithm, property testing, and sketching). We give a deterministic algorithm for finding this decomposition in almostlinear time. Previous algorithms are either randomized or take quadratic time. As a consequence, we resolve a major open problem if there is a deterministic dynamic connectivity algorithm with n^{0.4999} worstcase update time by giving an algorithm with n^{o(1)} worstcase update time. The result also implies almostlineartime deterministic algorithms for approximate max flow, electric flow, and Laplacian solvers. Joint work with Julia Chuzhoy, Yu Gao, Jason Li, Danupon Nanongkai, and Richard Peng. 
IGAFIT Algorithmic Colloquium #1
October 1, 2020 
An improved approximation algorithm for ATSP 
Vera Traub, ETH Zürich 
In a recent breakthrough, Svensson, Tarnawski, and Végh gave the first constantfactor approximation algorithm for the asymmetric traveling salesman problem (ATSP). In this work we revisit their algorithm. While following their overall framework, we improve on each part of it. Svensson, Tarnawski, and Végh perform several steps of reducing ATSP to more and more structured instances. We avoid one of their reduction steps (to irreducible instances) and thus obtain a simpler and much better reduction to vertebrate pairs. Moreover, we show that a slight variant of their algorithm for vertebrate pairs has a much smaller approximation ratio. Overall, we improve the approximation ratio from 506 to 22 + ε for any ε > 0. We also improve the upper bound on the integrality ratio of the standard LP relaxation from 319 to 22. This is joint work with Jens Vygen. 