Greedy Algorithms for Fair Division of Mixed Manna

We consider a multi-agent model for fair division of mixed manna (i.e. items for which agents can have positive, zero or negative utilities), in which agents have additive utilities for bundles of items. For this model, we give several general impossibility results and special possibility results for three common fairness concepts (i.e. EF1, EFX, EFX3) and one popular efficiency concept (i.e. PO). We also study how these interact with common welfare objectives such as the Nash, disutility Nash and egalitarian welfares. For example, we show that maximizing the Nash welfare with mixed manna (or minimizing the disutility Nash welfare) does not ensure an EF1 allocation whereas with goods and the Nash welfare it does. We also prove that an EFX3 allocation may not exist even with identical utilities. By comparison, with tertiary utilities, EFX and PO allocations, or EFX3 and PO allocations always exist. Also, with identical utilities, EFX and PO allocations always exist. For these cases, we give polynomial-time algorithms, returning such allocations and approximating further the Nash, disutility Nash and egalitarian welfares in special cases.

Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives

We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or the maximum cost of any agent is NP-hard. However, we show that the problem is fixed-parameter tractable, and the optimal solution can be computed in polynomial time whenever the number of facilities is bounded, or when all facilities have identical capacities. We then consider the problem from a mechanism design perspective where the agents are strategic and need not reveal their true locations. We show that several natural mechanisms studied in the uncapacitated setting either lose strategyproofness or a bound on the solution quality for the total or maximum cost objective. We then propose new mechanisms that are strategyproof and achieve approximation guarantees that almost match the lower bounds.

Online Fair Division: A Survey

We survey a burgeoning and promising new research area that considers the online nature of many practical fair division problems. We identify wide variety of such online fair division problems, as well as discuss new mechanisms and normative properties that apply to this online setting. The online nature of such fair division problems provides both opportunities and challenges such as the possibility to develop new online mechanisms as well as the difficulty of dealing with an uncertain future.

A Commentary on "Breaking Row and Column Symmetries in Matrix Models"

The CP 2002 paper entitled "Breaking Row and Column Symmetries in Matrix Models" by Flener et al. (https://link.springer.com/chapter/10.1007%2F3-540-46135-3_31) describes some of the first work for identifying and analyzing row and column symmetry in matrix models and for efficiently and effectively dealing with such symmetry using static symmetry-breaking ordering constraints. This commentary provides a retrospective on that work and highlights some of the subsequent work on the topic.

CSPLib: Twenty Years On

In 1999, we introduced CSPLib, a benchmark library for the constraints community. Our CP-1999 poster paper about CSPLib discussed the advantages and disadvantages of building such a library. Unlike some other domains such as theorem proving, or machine learning, representation was then and remains today a major issue in the success or failure to solve problems. Benchmarks in CSPLib are therefore specified in natural language as this allows users to find good representations for themselves. The community responded positively and CSPLib has become a valuable resource but, as we discuss here, we cannot rest.

SAT vs CSP: a commentary

In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs into SAT problems. For each mapping, I compared the impact of achieving arc-consistency on the CSP with unit propagation on the corresponding SAT problems, and lifted these results to CSP algorithms that maintain (some level of ) arc-consistency during search like FC and MAC, and to the Davis- Putnam procedure (which performs unit propagation at each search node). These results helped provide some insight into the relationship between propositional satisfiability and constraint satisfaction that set the scene for an important and valuable body of work that followed. I discuss here what prompted the paper, and what followed.

Verifying Properties of Binarized Deep Neural Networks

Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean satisfiability. Our main contribution is a construction that creates a representation of a binarized neural network as a Boolean formula. Our encoding is the first exact Boolean representation of a deep neural network. Using this encoding, we leverage the power of modern SAT solvers along with a proposed counterexample-guided search procedure to verify various properties of these networks. A particular focus will be on the critical property of robustness to adversarial perturbations. For this property, our experimental results demonstrate that our approach scales to medium-size deep neural networks used in image classification tasks. To the best of our knowledge, this is the first work on verifying properties of deep neural networks using an exact Boolean encoding of the network.

Deceased Organ Matching in Australia

Despite efforts to increase the supply of organs from living donors, most kidney transplants performed in Australia still come from deceased donors. The age of these donated organs has increased substantially in recent decades as the rate of fatal accidents on roads has fallen. The Organ and Tissue Authority in Australia is therefore looking to design a new mechanism that better matches the age of the organ to the age of the patient. I discuss the design, axiomatics and performance of several candidate mechanisms that respect the special online nature of this fair division problem.

Strategyproof Peer Selection using Randomization, Partitioning, and Apportionment

Peer review, evaluation, and selection is a fundamental aspect of modern science. Funding bodies the world over employ experts to review and select the best proposals of those submitted for funding. The problem of peer selection, however, is much more general: a professional society may want to give a subset of its members awards based on the opinions of all members; an instructor for a MOOC or online course may want to crowdsource grading; or a marketing company may select ideas from group brainstorming sessions based on peer evaluation. We make three fundamental contributions to the study of procedures or mechanisms for peer selection, a specific type of group decision-making problem, studied in computer science, economics, and political science. First, we propose a novel mechanism that is strategyproof, i.e., agents cannot benefit by reporting insincere valuations. Second, we demonstrate the effectiveness of our mechanism by a comprehensive simulation-based comparison with a suite of mechanisms found in the literature. Finally, our mechanism employs a randomized rounding technique that is of independent interest, as it solves the apportionment problem that arises in various settings where discrete resources such as parliamentary representation slots need to be divided proportionally.

Expert and Non-Expert Opinion about Technological Unemployment

There is significant concern that technological advances, especially in Robotics and Artificial Intelligence (AI), could lead to high levels of unemployment in the coming decades. Studies have estimated that around half of all current jobs are at risk of automation. To look into this issue in more depth, we surveyed experts in Robotics and AI about the risk, and compared their views with those of non-experts. Whilst the experts predicted a significant number of occupations were at risk of automation in the next two decades, they were more cautious than people outside the field in predicting occupations at risk. Their predictions were consistent with their estimates for when computers might be expected to reach human level performance across a wide range of skills. These estimates were typically decades later than those of the non-experts. Technological barriers may therefore provide society with more time to prepare for an automated future than the public fear. In addition, public expectations may need to be dampened about the speed of progress to be expected in Robotics and AI.