Seminario AGCO

The ACGO seminars are held every wednesday as part of an effort of a group of researchers around the topics of Algorithms, Combinatorics, Game Theory and Optimization. Our team consists of researchers in different disciplines and from several chilean universities. If you are interested in giving a talk or receiving the announcements of the seminars, please send us an email to jverschae followed by Webpage:

14:30 hrs.
Bhalchandra D. Thatte. Ufmg, Brazil.
Subgraph Posets and Graph Reconstruction
República 779 B, Sala 2do Piso.
14:30 hrs.
Andreas Tönnis. U. Chile
The Temp Secretary Problem and Extensions
República 779 B, Sala 3er Piso.
14:30 hrs.
Johannes Fischer. Tu Dortmund.
Simple, Fast and Lightweight Parallel Wavelet Tree Construction.
República 779 B, Sala 3er Piso.
14:30 hrs.
Claudio Telha Cornejo, Core & Om Partners.. Core, UC Louvain
A Competitive Uncapacitated Lot-Sizing Game
República 779 B, Sala 3er Piso
14:30 hrs.
Andrés Cristi. U Chile
A Near Optimal Mechanism for Energy Aware Scheduling
República 779 B, Sala 3er Piso.
14:30 hrs.
José Verschae. PUC
Symmetry and Hierarchies in Approximation Algorithms: Some Open Problems
República 779 B, Sala 3er Piso.
14:30 hrs.
Martin Matamala . Dim, U Chile.
An Extension of (Perfect) Matching
República 779 B, Sala 3er Piso.
14:30 hrs.
Antoine Hochart. U Chile
Ergodicity of Zero-Sum Stochastic Games
República 779 B, Sala 3er Piso.
14:30 hrs.
José Fuentes. Dcc, U Chile.
Fast and Compact Planar Embeddings
República 779 B, Sala 3er Piso.
14:30 hrs.hrs.
Miquel Oliu Barton. Université Paris-Dauphine.
The Unknown Stochastic Game
República 779 B, Sala 3er Piso.
Carlos Ochoa. U Chile
Synergistic Solutions on Multisets
Av República 779 B (Beauchef), Sala 3er Piso.
Karp et al. (1988) described Deferred Data Structures for Multisets as "lazy" data structures which partially sort data to support online rank and select queries, with the minimum amount of work in the worst case over instances of size $n$ and number of queries $q$ fixed. Barbay et al. (2016) refined this approach to take advantage of the gaps between the positions hit by the queries (i.e., the structure in the queries). We develop new techniques in order to further refine this approach and take advantage all at once of the structure (i.e., the multiplicities of the elements), some notions of local order (i.e., the number and sizes of runs) and global order (i.e., the number and positions of existing pivots) in the input; and of the structure and order in the sequence of queries. Our main result is a synergistic deferred data structure which outperforms all solutions in the comparison model that take advantage of only a subset of these features. As intermediate results, we describe two new synergistic sorting algorithms, which take advantage of some notions of structure and order (local and global) in the input, improving upon previous results which take advantage only of the structure (Munro and Spira 1979) or of the local order (Takaoka 1997) in the input; and one new multiselection algorithm which takes advantage of not only the order and structure in the input, but also of the structure in the queries.
Marc Schroder. U Chile
Claim Games for Estate Division Problems
Republica 779B, Sala P3, 3rd floor.

The estate division problem, also known as bankruptcy problem, concerns the issue of dividing an estate among a group of claimants when the sum of entitlements exceeds the size of the estate. This problem was formally introduced by O’Neill (1982), after which most of the literature focused on comparing different solution rules by means of their properties. We approach the problem strategically and analyse the claim game.

Kevin Schewior. U Chile / Max Planck Institute for Informatics
Chasing Convex Bodies
U Chile, Campus Beauchef, República 779 B, Sala 3er Piso
Krzysztof Fleszar. U Chile
Maximum Disjoint Paths: New Algorithms Based on Tree-Likeness
República 779 B, Sala 3er Piso (Beauchef)

Maximum Edge Disjoint Paths is a classical NP-hard problem of finding a maximum-size subset from a given set of k terminal pairs that can be routed via edge-disjoint paths.

One of the big open problems in approximation algorithms is to close the gap between the best known approximation upper bound of $\sqrt{n}$ (Chekuri et al. (2006)) and the best known lower bound of $2^{\sqrt{\log n}}$ (Chuzhoy et al. (2016)). In their seminal paper, Raghavan and Thompson (Combinatorica, 1987) introduce the technique of randomized rounding for LPs; their technique gives an O(1)-approximation when edges may be used by $O(\log n / \log\log n)$ paths.

In this talk, I introduce the problem and present two of our algorithms (ESA 2016) that strengthen the fundamental results above. They provide new bounds formulated in terms of the feedback vertex set number r of a graph, which measures its vertex deletion distance to a forest.

- An $O(\sqrt{r} \log{kr})}$-approximation algorithm. Up to a logarithmic factor, it strengthens the best known ratio $\sqrt{n}$ due to Chekuri et al., as $r \le n$.

- An $O(1)$-approximation algorithm with congestion bounded by $O(\log{kr} / \log\log{kr})$, strengthening the bound obtained by the classic approach of Raghavan and Thompson.

At the end, an open problem will be stated.

Saeed Hadikanlo. Univ. de Paris 9
Learning in Nonatomic Anonymous Games: Application To First Order Mean Field Games
República 779 B, Sala 3er Piso.
We introduce a model of anonymous games where the actions are chosen from possibly player dependent sets. We propose several learning procedures similar to the well-known Fictitious Play and Online Mirror Descent and prove their convergence to equilibrium under the classical monotonicity condition. Typical examples are First Order Mean Field Games.
Cristobal Guzman. PUC
Statistical Query Algorithms for Stochastic Convex Optimization
U Chile (Beauchef), Av Republica 701, Sala 33.
Statistical query (SQ) algorithms are the class of learning algorithms that can be implemented using approximate expectations of any given function of the input distribution, as opposed to direct access to i.i.d. samples. This computational model has a number of applications, ranging from noise-tolerant learning to differential privacy, and it has been used to obtain unconditional lower bounds on conjectured hard problems over distributions.
In this talk I will give an introduction to the theory of SQ algorithms, and we will see some recent developments in the case of stochastic convex optimization. Our main contribution is establishing nearly optimal SQ algorithms for mean vector estimation (this includes stochastic linear programming), which serves as a basis to obtain SQ versions of various gradient-type and polynomial time algorithms for stochastic convex optimization. Time permitting, I will show some consequences of our results for learning of halfspaces, differential privacy, and proving unconditional lower bounds on the power of convex relaxations for random constraint satisfaction problems.

This talk is based on joint work with Vitaly Feldman and Santosh Vempala, to appear in SODA 2017. 
Krzysztof Fleszar, Marc Schroder, Kevin Schewior. U Chile
Sesión de Problemas Abiertos
PUC, San Joaquín, Ciencias de la Salud SC403
Se darán 3 mini-charlas de aproximadamente 15 min cada una para después trabajar en los problemas. 

Krzysztof Fleszar: Edge Disjoint Paths
Marc Schroder: Negative prices in routing games
Kevin Schewior: Online Deadline Scheduling with Speed Augmentation
Fábio Botler. U Chile
Decomposing 8-Regular Graphs Into Paths of Length 4
U Chile (Beaucheff). Av Republica 701, Sala 33
A T-decomposition of a graph G is a set of edge-disjoint copies of T in G that cover the edge set of G. Graham and Häggkvist (1989) conjectured that any 2\ell-regular graph G admits a T-decomposition if T is a tree with \ell edges. Kouider and Lonc (1999) conjectured that, in the special case where T is the path with \ell edges, G admits a T-decomposition D where every vertex of G is the end-vertex of exactly two paths of D, and proved that this statement holds when G has girth at least (\ell + 3)/2. In this talk we verify Kouider and Lonc’s Conjecture (and, consequently, Graham-Häggkvist’s Conjecture) for paths of length 4.
Monaldo Mastrolilli. Idsia, Suiza
High Degree Sum of Squares Proofs/hierarchy for 0/1 Problems
U Chile (Beauchef), Av Republica 701, Sala 33
The Lasserre/Sum-of-Squares (SOS) hierarchy is a systematic procedure for constructing a sequence of increasingly tight semidefinite relaxations. It is known that the hierarchy converges to the 0/1 polytope in n levels and captures the convex relaxations used in the best available approximation algorithms for a wide variety of optimization problems.

In this talk I will give a gentle introduction of the SOS framework for 0/1 problems from a more general point of view.

I will point it out that this more general definition is needed for certain class of problems e removes some of the weakness of the standard SOS approach.
Bruno Ziliotto. Paris Dauphine University (Cnrs)
Limit Value in Zero-Sum Stochastic Games
U Chile (Beauchef) Av Republica 701, Sala 33
We consider a model of repeated game involving two adversary players, and where the state of nature is imperfectly observed. An old conjecture by Mertens (1986) predicted that in this model, when the game is repeated over and over, the optimal payoff of players should converge. We provide a counterexample to this conjecture.

No game theory prerequisite of any kind is needed to understand the talk.