IGAFIT Algorithmic Colloquium #11
|April 8, 2021|
|Fine-Grained Complexity of Optimization Problems|
|Karl Bringmann, Saarland University|
|Abstract: Fine-grained complexity theory is the area of theoretical computer science that proves conditional lower bounds based on conjectures such as the Strong Exponential Time Hypothesis. This enables the design of “best-possible” algorithms, where the running time of the algorithm matches a conditional lower bound.|
This talk surveys the developments of fine-grained complexity on classic optimization problems such as Subset Sum. In particular, since recently we know a best-possible algorithm for solving Subset Sum in pseudopolynomial time. We survey this result and the subsequent developments on approximation algorithms, output sensitive algorithms, and pseudopolynomial algorithms under different parameters. We also discuss extensions to other optimization problems such as Knapsack and Partition, scheduling, and integer linear programming.
|(to be posted soon) see the video: colloquium #11|
IGAFIT Algorithmic Colloquium #10
|March 25, 2021|
|Beyond Worst-Case Analysis|
|Tim Roughgarden, Columbia University|
|Abstract: One of the primary goals of the mathematical analysis of algorithms is to provide guidance about which algorithm is the “best” for solving a given computational problem. Worst-case analysis summarizes the performance profile of an algorithm by its worst performance on any input of a given size, implicitly advocating for the algorithm with the best-possible worst-case performance. Strong worst-case guarantees are the holy grail of algorithm design, providing an application-agnostic certification of an algorithm’s robustly good performance.|
However, for many fundamental problems and performance measures, such guarantees are impossible and a more nuanced analysis approach is called for. Research in “beyond worst-case analysis” develops alternatives to worst-case analysis, with applications ranging from clustering to linear programming to neural network training. This talk will highlight a mix of classic results, recent developments, and open questions in the area.
|see the video: colloquium #10|
IGAFIT Algorithmic Colloquium #9
|March 11, 2021|
|Graph Clustering Algorithms: Theoretical Insights For Practice|
|Vincent Cohen-Addad, Google Zürich|
|Abstract: A classic problem in machine learning and data analysis is to partition the vertices of a graph into very dense subgraphs with low expansion. In practice, the most popular approaches often rely on local search or greedy algorithms; not only for the ease of implementation, their scalability and their efficiency, but also because of the accuracy of these methods on many real world graphs. Even though we can’t prove that these algorithms have good performance guarantees in the worst-case, can we understand what make them so successful in practice? |
We review two popular objective functions — modularity and correlation clustering — and shed some light on the inner-workings of a popular heuristic (the so-called Louvain algorithm) by providing a “beyond worst-case” analysis. We then describe some key ideas to design graph clustering algorithms in massively parallel environments so as to optimize the above objective in only a constant number of rounds.
|see the video: colloquium #9|
IGAFIT Algorithmic Colloquium #8
|February 11, 2021|
|Deterministic Mincut in Almost-Linear Time|
|Jason Li, Carnegie Mellon University|
|We present a deterministic (global) mincut algorithm for weighted, undirected graphs that runs in m1+o(1) time, answering an open question of Karger from the 1990s. To obtain our result, we de-randomize the construction of the skeleton graph in Karger’s near-linear time mincut algorithm, which is its only randomized component. In particular, we partially de-randomize the well-known Benczur-Karger graph sparsification technique by random sampling, which we accomplish by the method of pessimistic estimators. Our main technical component is designing an efficient pessimistic estimator to capture the cuts of a graph, which involves harnessing the expander decomposition framework introduced in recent work by Goranci et al. (SODA 2021). As a side-effect, we obtain a structural representation of all approximate mincuts in a graph, which may have future applications.|
IGAFIT Algorithmic Colloquium #7
|January 28, 2021|
|Paths, cycles and beyond|
|Fedor V. Fomin, University of Bergen|
|I will speak about old and new parameterized algorithms for finding long paths and cycles in graphs. In particular, we discuss problems of finding paths and cycles whose lengths are beyond some “trivial” bounds.|
IGAFIT Algorithmic Colloquium #6
|December 10, 2020|
|Circulation control for faster minimum cost flow in unit-capacity 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 m4/3+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 well-known reductions, also implies improved running times for the shortest path problem with negative weights, minimum cost bipartite b-matching when |b|1 = O(m), and recovers the running time of the recent unit capacity maximum flow algorithm due to Liu-Sidford.
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 previously-arrived 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 Water-Filling algorithms to fully online matching and its fractional relaxation respectively. The former is 0.521-competitive in general graphs, and 0.567-competitive 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 <(1-1/e)-competitive in fully online matching even for bipartite graphs. Finally, we introduce new algorithms that are strictly better than Ranking and Water-Filling 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 3/2-ε approximation algorithm for metric TSP, for some ε>10-36. This slightly improves over the classical 3/2 approximation algorithm due to Christofides  and Serdyukov . 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 almost-linear 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 almost-linear 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 n0.4999 worst-case update time by giving an algorithm with no(1) worst-case update time. The result also implies almost-linear-time 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 constant-factor 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.
Follow us also on twitter and facebook. (To subscribe to the ICAFIT Algorithmic Colloquium mailing list with announcements send an email to email@example.com with subject SUBSCRIBE.)