Algorithms and Complexity
https://csd.cs.cmu.edu/
enAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2024-04-25
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-04-25T15:00:00-04:00" title="Thursday, April 25, 2024 - 15:00">Thu, 04/25/2024 - 15:00</time>
</span>
In Person
Perfect matchings in the random bipartite geometric graph
XAVIER PÉREZ GIMÉNEZ
<p>We consider the standard random bipartite geometric graph process in which n red vertices and n blue vertices are placed at random on the unit d-dimensional cube and edges are added sequentially, between vertices of different colors, in increasing order of edge-length. A natural question is to ask whether the first edge in the process that results in the minimum degree being at least one coincides, with high probability, with the first edge that creates a perfect matching. While this was already known to be false when d=2, as the thresholds are not even of the same order, we are able to positively answer it for dimension d at least 3. </p><p><em>This is joint work with Abigail Raz. </em></p><p><em>Tea and cookies at 4pm in the Math Lounge, Wean 6220 (bring your own cup if possible)</em></p>
<time datetime="2024-04-25T19:00:00Z">April 25, 2024 3:00pm</time>
<time datetime="2024-04-25T20:00:00Z">April 25, 2024 4:00pm</time>
https://math.unl.edu/xperezgimenez2
Associate Professor, Department of Mathematics, University of Nebraska-Lincoln
https://aco.math.cmu.edu/abs-23-24/apr25.html
<a href="mailto:alanlew@andrew.cmu.edu">alanlew@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cs.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean Hall 8220
Thu, 25 Apr 2024 19:00:00 +0000Anonymous222334912 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2024-04-04
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-04-04T15:00:00-04:00" title="Thursday, April 4, 2024 - 15:00">Thu, 04/04/2024 - 15:00</time>
</span>
In Person
Random Matching Markets
PAWEL PRALAT
<p>Stable matching mechanisms are ubiquitous in theory and in practice, with centralized mechanisms used to match students to schools or medical residents to hospitals. It is known that imbalance in the number of agents on either side of a random matching market has a profound effect on the market’s expected characteristics. The "long side" (i.e. the side with a greater number of agents) receives significantly worse matches in expectation than the “short side”. As a result, agents on the long side have very little market power, and must settle for a match which is not much better than a random assignment. During the talk, I will discuss classical results and present a new proof that analyzes the most natural algorithm (“long side proposing”) producing the optimal stable outcome. This new proof, arguably, provides a better intuition for this surprising huge advantage of the short side. </p><p><em>4:00 pm → tea and cookies in the math lounge (bring your own mug if you have one), Wean 6220</em></p>
<time datetime="2024-04-04T19:00:00Z">April 4, 2024 3:00pm</time>
<time datetime="2024-04-04T20:00:00Z">April 4, 2024 4:00pm</time>
https://math.ryerson.ca/~pralat/
Professor, Department of Mathematics, Toronto Metropolitan University
https://aco.math.cmu.edu/abs-23-24/apr04.html
<a href="mailto:alanlew@andrew.cmu.edu">alanlew@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Wean Hall 8220
Thu, 04 Apr 2024 19:00:00 +0000Anonymous222334511 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2024-03-28
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-03-28T15:00:00-04:00" title="Thursday, March 28, 2024 - 15:00">Thu, 03/28/2024 - 15:00</time>
</span>
In Person
Isomorphisms between dense random graphs.
LUTZ WARNKE
<p>Applied benchmark tests for the famous 'subgraph isomorphism problem' empirically discovered interesting phase transitions in random graphs. This motivates our rigorous study of two variants of the induced subgraph isomorphism problem for two independent binomial random graphs with constant edge-probabilities <em>p<sub>1</sub>, p<sub>2</sub></em>. In particular, (i) we prove a sharp threshold result for the appearance of <em>G<sub>n,p1</sub></em> as an induced subgraph of <em>G<sub>n,p2</sub></em>, (ii) we show two-point concentration of the size of the maximum common induced subgraph of <em>G<sub>n,p1</sub></em> and <em>G<sub>n,p2</sub></em>, and (iii) we show that the number of induced copies of<em> G<sub>n,p1</sub></em> in <em>G<sub>n,p2</sub></em> has an unusual 'squashed lognormal' limiting distribution. </p><p>These results confirm simulation-based predictions of McCreesh, Prosser, Solnon and Trimble, and resolve several open problems of Chatterjee and Diaconis. The proofs are based on careful refinements of the first and second moment method, using extra twists to (a) take some non-standard behaviors into account, and (b) work around the large variance issues that prevent standard applications of the second moment method, using in particular pseudorandom properties and multi-round exposure arguments to tame the variance. </p><p><em>Based on </em><a href="https://arxiv.org/abs/2305.04850" target="_blank"><em>joint work with Erlang Surya and Emily Zhu</em></a></p>
<time datetime="2024-03-28T19:00:00Z">March 28, 2024 3:00pm</time>
<time datetime="2024-03-28T20:00:00Z">March 28, 2024 4:00pm</time>
https://mathweb.ucsd.edu/people/profiles/lutz-warnke
Associate Professor, Department of Mathematics, University of California, San Diego
https://aco.math.cmu.edu/abs-23-24/mar28.html
<a href="mailto:alanlew@andrew.cmu.edu">alanlew@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Wean Hall 8220
Thu, 28 Mar 2024 19:00:00 +0000Anonymous222334452 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2024-03-07
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-03-07T15:00:00-05:00" title="Thursday, March 7, 2024 - 15:00">Thu, 03/07/2024 - 15:00</time>
</span>
In Person
A hypergraph bipartite Turan problem with odd uniformity
JIE MA
<p>In this paper, we investigate the hypergraph Turán number ex(n,K(r)s,t). Here, K(r)s,t denotes the r-uniform hypergraph with vertex set (∪i∈[t]Xi)∪Y and edge set {Xi∪{y}:i∈[t],y∈Y}, where X1,X2,⋯,Xt are t pairwise disjoint sets of size r−1 and Y is a set of size s disjoint from each Xi. This study was initially explored by Erdős and has since received substantial attention in research. Recent advancements by Brada\v{c}, Gishboliner, Janzer and Sudakov have greatly contributed to a better understanding of this problem. They proved that ex(n,K(r)s,t)=Os,t(nr−1s−1) holds for any r≥3 and s,t≥2. They also provided constructions illustrating the tightness of this bound if r≥4 is {\it even} and t≫s≥2. Furthermore, they proved that ex(n,K(3)s,t)=Os,t(n3−1s−1−εs) holds for s≥3 and some ϵs>0. Addressing this intriguing discrepancy between the behavior of this number for r=3 and the even cases, Bradač et al. post a question of whether ex(n,K(r)s,t)=Or,s,t(nr−1s−1−ε) holds for odd r≥5 and any s≥3. In this paper, we provide an affirmative answer to this question, utilizing novel techniques to identify regular and dense substructures. This result highlights a rare instance in hypergraph Turán problems where the solution depends on the parity of the uniformity.</p>
<time datetime="2024-03-07T20:00:00Z">March 7, 2024 3:00pm</time>
<time datetime="2024-03-07T21:00:00Z">March 7, 2024 4:00pm</time>
http://staff.ustc.edu.cn/~jiema/
Professor, School of Mathematical Sciences, University of Science and Technology of China
https://aco.math.cmu.edu/abs-23-24/mar07.html
<a href="mailto:alanlew@andrew.cmu.edu">alanlew@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Wean Hall 8220
Thu, 07 Mar 2024 20:00:00 +0000Anonymous222334341 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2024-02-08
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-02-08T15:00:00-05:00" title="Thursday, February 8, 2024 - 15:00">Thu, 02/08/2024 - 15:00</time>
</span>
In Person
Some results and open questions in random structures
ALAN FRIEZE
<p>We review some results and open questions on (i) the cover time of random graphs, (ii) edge colored random graphs, (iii) optimization problems on edge-weighted graphs. </p><p><em>4:00 pm - Tea and cookies in the Math Lounge - Wean 6220</em></p>
<time datetime="2024-02-08T20:00:00Z">February 8, 2024 3:00pm</time>
<time datetime="2024-02-08T21:00:00Z">February 8, 2024 4:00pm</time>
https://www.math.cmu.edu/~af1p/
University Professor, Department of Mathematical Sciences, Carnegie Mellon University
https://aco.math.cmu.edu/abs-23-24/feb08.html
<a href="mailto:martap@andrew.cmu.edu">martap@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/people/faculty/alan-frieze" hreflang="en">Alan Frieze</a>
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Wean Hall 8220
Thu, 08 Feb 2024 20:00:00 +0000Anonymous222334202 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2024-01-25
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-01-25T15:00:00-05:00" title="Thursday, January 25, 2024 - 15:00">Thu, 01/25/2024 - 15:00</time>
</span>
In Person
Finding balance in random forests
WESLEY PEGDEN
<p>There has been a surge in interest in algorithms that sample balanced contiguous partitions of geometric regions, due to the use of such algorithms in the analysis of political districtings. Most approaches to the problem use Markov chains of various types, which in almost no practical case are known to be rapidly mixing. But recent breakthroughs in matroid theory enable highly efficient sampling of random forests, and Charikar, Liu, Liu, and Vuong conjectured that at least for grid graphs, a 1/poly fraction of random forests on k components (k a constant) have balanced component sizes. </p><p>The key implication of their conjecture is that for grid graphs, there is a polynomial-time algorithm to sample from the /spanning-tree distribution/ on balanced partitions, which weights each balanced partition according to the product of the number of spanning trees of each partition class. We confirm their conjecture, and also prove that random forests of grid-like graphs have a 1/poly chance of having approximately balanced component sizes. The proofs make use of Wilson's random spanning tree algorithm, and leverage geometric properties of random walk in lattices. </p><p><em>Tea and cookies after the talk</em> i<em>n Wean 6220 (bring your own mug if you have one).</em></p>
<time datetime="2024-01-25T20:00:00Z">January 25, 2024 3:00pm</time>
<time datetime="2024-01-25T21:00:00Z">January 25, 2024 4:00pm</time>
https://www.math.cmu.edu/~wes/
Associate Professor, Department of Mathematics, Carnegie Mellon University
https://aco.math.cmu.edu/abs-23-24/jan25.html
<a href="mailto:martap@andrew.cmu.edu">martap@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Wean Hall 8220
Thu, 25 Jan 2024 20:00:00 +0000Anonymous222334123 at https://csd.cs.cmu.eduOperations Research Seminar
https://csd.cs.cmu.edu/calendar/seminar-Operations-Research-2023-
<span>Operations Research Seminar</span>
Tepper 4242
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2023-12-08T13:30:00-05:00" title="Friday, December 8, 2023 - 13:30">Fri, 12/08/2023 - 13:30</time>
</span>
In Person
Polyhedral Formulations for (Subset) Feedback Vertex Set
CHANDRA CHEKURI
<p>We consider feedback vertex set (FVS) in undirected graphs, and its generalization the subset feedback vertex set (SFVS) problem. In FVS the input is a vertex-weighted graph G=(V,E) and the goal is to remove a minimum weight susbet of vertices S such that the G-S has no cycles. In SFVS we are also given a subset T of the vertices called terminals, and the goal is to remove a minimum weight subset of vertices S such that G-S has no cycle containing a terminal. FVS is a well-known NP-Hard problem and admits a 2-approximation from several decades ago via the local-ratio method (Bafna et al, Becker and Geiger). Moreover 2 is the best approximation ratio one can hope for assuming the unique games conjecture. Chudak et al. developed an LP relaxation for FVS and interpreted the local-ratio algorithms as primal-dual algorithms with respect to this relaxation. However, their LP relaxation was not known to be solvable in polynomial time.</p>
<p>We develop a new LP relaxation that is poly-time solvable and has an integrality gap of 2. This LP relaxation is based on a connection to a relaxation for densest subgraph by Charikar. A few years ago Chekuri and Madan developed a poly-time solvable LP relaxation for the more general SFVS problem and they showed that it had an integrality gap of at most 13 via a rounding algorithm. They raised the question of whether their LP relaxation had an integrality gap of at most 2 for FVS (and also SFVS). We answer this question in the affirmative for FVS. Despite proving that these two LP relaxations (which come from different perspectives on the problem) have an integrality gap of at most 2 for FVS, we do not know a direct way to round the relaxations to achieve this bound. We conjecture an extreme point property for one of the LP relaxations that would allow one to obtain an iterated rounding 2-approximation algorithm, and provide evidence for this conjecture via a related result for the pseudo-forest deletion set problem.</p>
<p>The goal of the talk is to highlight the ideas and connections behind the several LP relaxations for these problems, and to point out several open problems.</p>
<p><em>Based on joint work with <a href="https://arxiv.org/abs/2303.12850" target="_blank">Karthik Chandrasekharan, Samuel Fiorini, Shubhang Kulkarni, and Stefan Weltge</a> , and an <a href="https://epubs.siam.org/doi/10.1137/1.9781611974331.ch58" target="_blank">older paper with Vivek Madan</a> </em></p>
<p>—</p>
<p><a href="http://chekuri.cs.illinois.edu/" target="_blank">Chandra Chekuri</a> is the Paul and Cynthia Saylor Professor in the Department of Computer Science at University of Illinois, Urbana-Champaign. He joined the university in 2006 after spending eight years at Lucent Bell Labs. Prior to that he received his PhD from Stanford University and an undergraduate degree from IIT Chennai. He is interested in the design and analysis of algorithms, combinatorial optimization, and theoretical computer science. He is happy about some of his contributions to (fast) approximation algorithms, graphs and networks, scheduling, and optimizing with submodular functions.</p>
<time datetime="2023-12-08T18:30:00Z">December 8, 2023 1:30pm</time>
<time datetime="2023-12-08T19:30:00Z">December 8, 2023 2:30pm</time>
http://chekuri.cs.illinois.edu/
Paul and Cynthia Saylor Professor, Algorithms / Theory Group, Department of Computer Science, University of Illinois, Urbana-Champaign
<a href="mailto:pconley@andrew.cmu.edu">pconley@andrew.cmu.edu</a>
Seminar
<a href="https://csd.cs.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Tepper 4242
Fri, 08 Dec 2023 18:30:00 +0000Anonymous222332676 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2023-12-07
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2023-12-07T15:30:00-05:00" title="Thursday, December 7, 2023 - 15:30">Thu, 12/07/2023 - 15:30</time>
</span>
In Person
Optimal Scheduling of Elastic and Inelastic Jobs
BEN BERG
<p>A wide range of modern computer systems rely on parallelism to process jobs quickly. Unlike the jobs considered in most classical scheduling problems, parallelizable jobs can be completed more quickly when they are run on multiple servers or cores. However, not all jobs are perfectly parallelizable. Computing workloads are typically composed of a mixture of highly parallelizable elastic jobs and less parallelizable inelastic jobs. Given a fixed number of cores, it is not obvious how to best allocate cores across a stream of arriving elastic and inelastic jobs. We consider the problem of allocating cores to jobs in order to minimize the mean response time across jobs — the average time from when a job arrives to the system until it is complete.</p>
<p>To solve this problem, one must balance a tradeoff between prioritizing short jobs and deferring parallelizable work. Completing short jobs before long jobs is known to reduce the mean response time in many systems. However, when jobs are parallelizable, it is also important to keep some elastic jobs in the system to ensure that the available cores remain utilized. Hence, it can also be beneficial to prioritize longer inelastic jobs ahead of shorter elastic jobs. Using coupling arguments and Lyapunov drift arguments from queueing theory, we show how to optimally balance this tradeoff. Specifically, we show how the optimal core allocation policy depends on the number of cores in the system, the system load, and the distributions of elastic and inelastic job sizes.</p>
<time datetime="2023-12-07T20:30:00Z">December 7, 2023 3:30pm</time>
<time datetime="2023-12-07T21:30:00Z">December 7, 2023 4:30pm</time>
https://cs.unc.edu/person/benjamin-berg/
Assistant Professor, Computer Science Department, University of North Carolina at Chapel Hill,
https://aco.math.cmu.edu/abs-23-24/dec07.html
<a href="mailto:martap@andrew.cmu.edu">martap@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cs.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean 8220
Thu, 07 Dec 2023 20:30:00 +0000Anonymous222332674 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2023-11-30
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2023-11-30T15:30:00-05:00" title="Thursday, November 30, 2023 - 15:30">Thu, 11/30/2023 - 15:30</time>
</span>
In Person
On relaxations of “rank” for boolean matrices
KKAVE HOSSEINI
<p>In this talk I will discuss a few well-known complexity parameters for boolean matrices that are relaxations of rank (over the reals). These are approximate rank, sign-rank/dimension complexity, margin/discrepancy, gamma2 norm, and approximate-gamma2. The focus of this talk is to study the meta-question: "what is the relationship between these parameters?". It turns out that study of this meta-question connects many different areas and equivalent stories are to be told in learning theory, communication complexity, convex geometry, theory of dimensionality reduction, etc. I will try to answer some of these pairwise relations using different tools such as Fourier analysis, topology, and also ideas from discrete geometry.</p>
<p><em>Refreshments — 3:00 pm, Math Lounge / Wean 6220</em></p>
<time datetime="2023-11-30T20:30:00Z">November 30, 2023 3:30pm</time>
<time datetime="2023-11-30T21:30:00Z">November 30, 2023 4:30pm</time>
https://www.cs.rochester.edu/u/shossei2/
Assistant Professor, Department of Computer Science, University of Rochester
https://aco.math.cmu.edu/abs-23-24/nov30.html
<a href="mailto:martap@andrew.cmu.edu">martap@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cs.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean 8220
Thu, 30 Nov 2023 20:30:00 +0000Anonymous222332654 at https://csd.cs.cmu.eduAlgorithms, Combinatorics and Optimization Seminar
https://csd.cs.cmu.edu/calendar/seminar-series-ACO-2023-11-16
<span>Algorithms, Combinatorics and Optimization Seminar</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2023-11-16T15:30:00-05:00" title="Thursday, November 16, 2023 - 15:30">Thu, 11/16/2023 - 15:30</time>
</span>
In Person
Using slice-rank and partition-rank
MOHAMED OMAR
<p>Recent breakthroughs in combinatorics, especially on bounds of sizes of sets avoiding particular configurations, have been afforded by the slice-rank and partition-rank methods. In this talk we introduce these concepts and the challenges that arise when using them, in hopes that audience members have access to a new tool they may find useful in their own work. Furthermore we discuss the work of the speaker in integrating partition lattices into the theory.</p>
<time datetime="2023-11-16T20:30:00Z">November 16, 2023 3:30pm</time>
<time datetime="2023-11-16T21:30:00Z">November 16, 2023 4:30pm</time>
https://www.yorku.ca/science/mathstats/faculty-and-instructors/
Professor, Department of Mathematics and Statistics, York University
https://aco.math.cmu.edu/abs-23-24/nov16.html
<a href="mailto:martap@andrew.cmu.edu">martap@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cs.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
Wean Hall 8220
Thu, 16 Nov 2023 20:30:00 +0000Anonymous222332587 at https://csd.cs.cmu.edu