Location: SIT 459

Speaker: Hubert Chan, The University of Hong Kong

Title: Revisiting Diffusion Process for Hypergraph Laplacian

Abstract:

Hypergraph Laplacian has been defined via a diffusion process [Louis STOC 2015]. The spectral properties of the Laplacian is used to achieve a variant of the Cheeger’s inequality for hyperedge expansion and higher-order Cheeger-like inequalities for multi-way expansion.

In this talk, we take a closer look at this diffusion process, in which each hyperedge tries to transfer measure from vertices having maximum measure to those having minimum. In order for the diffusion process to be well-defined, we see that the hyperedges must be coordinated to essentially solve a densest subset problem.

Consequently, we can recover the basic Cheeger’s inequality, but higher-order spectral properties of the Laplacian do not hold in hypergraphs in general.

This is joint work with Anand Louis, Zhihao Gavin Tang and Chenzi Zhang.

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Location: SIT 459

Speaker: Nengkun Yu, University of Technology Sydney

Title: Learning classical information in Quantum system—from Pretty Good Measurement to Pretty Good Tomography

Abstract:

We start with a promise problem of extracting information from a single quantum system whose state is known to be in one of several possible states. In the generic case, it is notoriously difficult to find the optimal measurement (learning algorithm), that is the measurement that provides the most possible information about the system’s state. A simple general prescription for a measurement, pretty good measurement, is provided, which is typically not optimal but appears to be quite good.

In early 1970s, A. Holevo (winner of the Claude E. Shannon Award 2016) initiated the study of the problem of quantum state tomography to obtain complete classical information of the unknown quantum system, when i.i.d. copies of the quantum system is provided. This is the quantum analogue of the problem of estimating a probability distribution given some number of samples. Moreover, it could also be viewed as a special and fundamental problem in quantum property testing, the study of which has recently attracted much attention.

We designed an efficient learning algorithm scheme for this problem by generalised the pretty good measurement into pretty good tomography. The optimality of this algorithm is shown by putting this problem into a quantum communication scenario and employing quantum communication complexity bounds as a tool.

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Location: SIT 459

Speaker: Patrick Eades

Title: Stochastic k-center and j-flats

Abstract: Patrick will present the paper “Stochastic k-center and j-flats” by Lingxiao Huang and Jian Li.

“Solving geometric optimization problems over uncertain data have become increasingly important in many applications and have attracted a lot of attentions in recent years. In this paper, the authors study two important geometric optimization problems, the k-center problem and the j-flat-center problem, over stochastic/uncertain data points in Euclidean spaces.”

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Location: SIT 459

Speaker: Haris Aziz, Data61/CSIRO and UNSW

Title: Justified Representation in Approval- Based Committee Voting

Abstract:

We consider approval-based committee voting, i.e. the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits agreement by supporting the same candidate, then at least one voter in this group has an approved candidate in the winning committee. We show that for every list of ballots it is possible to select a committee that provides JR. However, it turns out that several prominent approval-based voting rules may fail to output such a committee. We then introduce a stronger version of the JR axiom, which we call extended justified representation (EJR) that characterizes PAV — a known committee voting rule. We also consider several related questions including the complexity of associated computational problems.

(Based on joint work with Markus Brill, Vincent Conitzer, Edith Elkind, Rupert Freeman, and Toby Walsh)

Bio:

Haris Aziz is a senior research scientist at Data61, CSIRO and a conjoint senior lecturer at the University of New South Wales, Sydney. His research interests lie at the intersection of artificial intelligence, theoretical computer science, and economics.

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Location: SIT 459

Speaker: Jonathan Chung, University of Sydney

Title: Computing the Yolk in Spatial Voting Games

Abstract:

The spatial model of voting describes a set of voters with Euclidean preferences on a multidimensional space of policies. A game within this model can be played as follows: given two candidates competing for the support of these voters, the objective is to find a point on the space such that no other point is preferred by more voters. However, in most voter configurations such a point is unlikely to occur. This motivates the idea of a yolk, which is a closed ball such any point inside the ball is preferred to by more voters than any point outside it. We show in a two-dimensional setting that the yolk is deterministically computable in O(n^(4/3) log^(2/3) n) time, and propose a (1 + epsilon)-approximation that can find the yolk in O(n log^3 n) time.

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Location: SIT 459

Speaker: Michael Rizzuto, University of Sydney

Title: Reduction of the Radius of a Graph by Adding Edges

Abstract:

Given a graph and a maximum number of extra edges, we wish to find the minimum radius achievable by adding these edges to the graph.

A solution for trees was found through a greedy algorithm, and a solution for general graphs was obtained through the use of a tree decomposition and dynamic programming.

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Location: SIT 459

Speaker: Andrew Cherry, University of Sydney

Title: Approximation Algorithms for 2D Barrier Coverage

Abstract:

Given barriers represented by line segments and sensors with circular radius initially located in arbitrary locations we want to move a group of sensors to arbitrary locations on the barriers so that the barriers are completely covered and the sum of sensor movements is minimised. This problem is NP-complete.

We find approximation algorithms that allow solutions when sensors have uniform radii.

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Location: SIT 459

Speaker: Prof. Sándor Fekete, TU Braunschweig

Title: Algorithms for robot navigation: From optimizing individual

robots to particle swarms

Abstract:

Planning and optimizing the motion of one or several robots poses a wide range of problems.

What positions should one powerful robot pick to scan a given area with obstacles?

How can we coordinate a group of weaker robots to explore an unknown environment?

How can we ensure that a swarm of very simple robots with local capabilities can deal with conflicting global requirements?

And how can a particle swarm perform complex operations? We will demonstrate how an appropriate spectrum of algorithmic methods in combination with geometry can be used to achieve progress on all of these challenges.

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Location: SIT 459

Speaker: Shenwei Huang, UNSW

Title: Colouring on hereditary graph classes

Abstract:

A graph class is hereditary if it is closed under taking induced subgraphs. It is known that hereditary classes can be characterized by forbidden induced subgraphs. We survey some recent complexity results on colouring on hereditary classes, mainly focusing on graphs that do not contain a path on t vertices for any fixed t. If time permitted, we will also talk about a result on colouring even-hole-free graphs, i.e., graphs that do not contain any cycle of even length as an induced subgraph.

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**Workshop description**

Algorithms and data structures form a key component of any software system. Many algorithmic problems arising in practice are intractable, which means there are no fast algorithm solving these problems optimally on all problem instances. The area of fixed-parameter tractability tries to gain more insight into such problems, by analyzing them in terms of some well-defined parameter(s) that capture the difficulty of the problem. In many applications, algorithms are needed for problems involving spatial data. Computational geometry is the area within algorithm research dealing with spatial data. This workshop brings together researchers from the areas of computational geometry and fixed-parameter tractability, to advance the study of intractable problems on spatial data.

**Dates and time**

The workshop will start at 10am on Tuesday the 6th of December and end at 3pm on Friday the 9th of December.

**Venue**

The workshop will be hosted by the School of Information Technologies at University of Sydney.

**Address:** Lecture theatre 123, School of Information Technologies, University of Sydney, building J12, 1 Cleveland Street, Darlington NSW 2008, Australia.

**Tentative schedule**

Tuesday

- 10am: Workshop starts (open problem session)
- 1pm: Lunch at The Rose Hotel
- 2:30pm Transport to Clovelly
- 3pm-6pm: Lawn bowl at Clovelly Lawn Bowl Club (Clovelly also has excellent snorkelling!)
- 7pm: Dinner at Farinha‘s in Coogee

Wednesday

- 9:30am-12:30pm: Open problems and research discussion
- 12:30pm-1:30pm: Lunch at Goen Japanese Restaurant
- 1:30pm-5pm: Research discussion

Thursday

- 9:30am-12:30pm: Open problems and research discussion
- 12:30pm-1:30pm: Lunch at Thai Tha Hai
- 1:30pm-5pm: Research discussion
- 7pm: Workshop dinner at Rubyo’s

Friday

- 9:30am-12:30pm: Research discussion
- 12:30pm-1:30pm: Lunch at Baja Cantina
- 2pm-3pm: Progress report
- 3pm: End of workshop

**List of tentative participants**

- Akanksha Agrawal, University of Bergen
- Haris Aziz, UNSW/Data61
- Katrin Casel, University of Trier
- Hubert Chan, University of Hong Kong
- Man Kwun Chiu, National Institute of Informatics
- Michael R. Fellows, University of Bergen
- Serge Gaspers, UNSW/Data61
- Joachim Gudmundsson, University of Sydney
- Shenwei Huang, UNSW
- Paul Hunter, UNSW
- Matias Korman, Tohoku University
- Luke Mathieson, University of Newcastle
- Saeed Mehrabi, University of Waterloo
- Julián Mestre, University of Sydney
- Matthias Mnich, University of Bonn
- André van Renssen, National Institute of Informatics
- Marcel Roeloffzen, National Institute of Informatics
- Frances A. Rosamond, University of Bergen
- Stefan Rümmele, University of Sydney/UNSW
- Abdallah Saffidine, UNSW
- Mingyu Xiao, University of Electronic Science and Technology of China

**Related activities**

- ISAAC 2016, 12-14 December 2016 in Sydney, Australia
- ACCMCC 2016, 12-16 December in Newcastle, Australia
- APCO 2016, 16-17 December in Newcastle, Australia

**Local organizer**

- Joachim Gudmundsson, University of Sydney (Contact number: +61 (0)4 2307 0859)
- Serge Gaspers, UNSW/Data61
- Stefan Rümmele, University of Sydney/UNSW
- Julián Mestre, University of Sydney

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