New Zealand


We study the NP-hard Fair Connected Districting problem: Partition a vertex-colored graph into k connected components (subsequently referred to as districts) so that in every district the most frequent color occurs at most a given number of times more often than the second most frequent color. Fair Connected Districting is motivated by various real-world scenarios, such as district-based elections, where agents of different types, which are one-to-one represented by nodes in a network, have to be partitioned into disjoint districts. We conduct a fine-grained analysis of the (parameterized) computational complexity of Fair Connected Districting: We study its parameterized complexity with respect to various graph parameters, including treewidth, and problem-specific parameters, including the numbers of colors and districts, and its complexity on graphs from different classes (such as paths, stars, and trees).

AAMAS 2022

A Refined Complexity Analysis of Fair Districting over Graphs

electoral districting

parameterized algorithmics

fairness

AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

The AAMAS conference series was initiated in 2002 in Bologna, Italy as a joint event comprising the 6th International Conference on Autonomous Agents (AA), the 5th International Conference on Multiagent Systems (ICMAS), and the 9th International Workshop on Agent Theories, Architectures, and Languages (ATAL).

Subsequent AAMAS conferences have been held in Melbourne, Australia (July 2003), New York City, NY, USA (July 2004), Utrecht, The Netherlands (July 2005), Hakodate, Japan (May 2006), Honolulu, Hawaii, USA (May 2007), Estoril, Portugal (May 2008), Budapest, Hungary (May 2009), Toronto, Canada (May 2010), Taipei, Taiwan (May 2011), Valencia, Spain (June 2012), Minnesota, USA (May 2013), Paris, France (May 2014), Istanbul, Turkey (May 2015), Singapore (May 2016), São Paulo (2017) and Stockholm, Sweden (2018), Montreal (May 2019), Auckland (May 2020, Virtual), London (May 2021, Virtual).
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AAMAS (International Conference on Autonomous Agents and Multiagent Systems) is the largest and most influential conference in the area of agents and multiagent systems. The aim of the conference is to bring together researchers and practitioners in all areas of agent technology and to provide a single, high-profile, internationally renowned forum for research in the theory and practice of autonomous agents and multiagent systems. AAMAS is the flagship conference of the non-profit International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

poster


Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the input characteristics of the second one. We investigate the connection between stability, popularity, and their strict variants, strong stability and strong popularity in three-dimensional instances with cyclic preferences. Furthermore, we also derive results on the complexity of these problems when the preferences are derived from master lists.

Three-Dimensional Popular Matching with Cyclic Preferences

We consider the well-studied many-to-one bipartite matching problem of assigning applicants $\A$ to posts $\B$ where applicants rank posts in the order of preference. This setting models many important real-world allocation problems like assigning students to courses, applicants to jobs, amongst many others. In such scenarios, it is natural to ask for an allocation that satisfies guarantees of the form ``match at least 80\% of applicants to one of their top three choices'' or ``it is unacceptable to leave more than 10\% of applicants unassigned''. The well-studied notions of rank-maximality and fairness fail to capture such requirements due to their property of optimizing extreme ends of the {\em signature} of a matching. We, therefore, propose a novel optimality criteria, which we call as the ``cumulative better signature''.

We investigate the computational complexity of the new notion of optimality in the setting where posts have associated {\em fixed} quotas. We prove that under the fixed quota setting, the problem turns out to be NP-hard under severe restrictions. We provide randomized algorithms in the fixed quota setting when the number of ranks is constant. We also study the problem under a {\em cost-based quota} setting and show that min-cost cumulative better matching can be computed efficiently. Apart from circumventing the hardness, the cost-based quota setting is motivated by real-world applications like course allocation, school choice where the capacities or quotas need not be rigid.

Optimal Matchings with One-Sided Preferences: Fixed and Cost-Based Quotas

The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint sets of agents wherein no pair of agents prefer each other to their matched partners. The Deferred Acceptance (DA) algorithm is an elegant procedure that guarantees a stable matching for any input; however, its outcome may be unfair as it always favors one side by returning a matching that is optimal for one side (say men) and pessimal for the other side (say women). A desirable fairness notion is minimizing the sex-equality cost, i.e. the difference between the total rankings of both sides. Computing such stable matchings is a strongly NP-hard problem, which raises the question of what tractable algorithms to adopt in practice. We conduct a series of empirical evaluations on the properties of sex-equal stable matchings when preferences of agents on both sides are correlated. Our empirical results suggest that under correlated preferences, the DA algorithm returns stable matchings with low sex-equality cost, which further confirms its broad use in many practical applications.

Fair Stable Matching Meets Correlated Preferences

To overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patient-donor pools. We consider a recent credit system where in each round, countries are given an initial kidney transplant allocation which is adjusted by a credit function yielding a target allocation. The goal is to find a solution in the patient-donor compatibility graph that approaches the target allocation as closely as possible, to ensure long-term stability of the international pool. As solutions, we use maximum matchings that lexicographically minimize the country deviations from the target allocation. We first give a polynomial-time algorithm for computing such matchings. We then perform, for the first time, a computational study for a {\it large} number of countries. For the initial allocations we use, besides two easy-to-compute solution concepts, two classical concepts: the Shapley value and nucleolus. These are hard to compute, but by using state-of-the-art software we show that they are now within reach for IKEPs of up to fifteen countries. Our experiments show that using lexicographically minimal maximum matchings instead of ones that only minimize the largest deviation from the target allocation (as previously done) may make an IKEP up to 52\% more balanced.

Computing Balanced Solutions for Large International Kidney Exchange Schemes


In multi-objective optimization, learning all the policies that reach Pareto-efficient solutions is an expensive process. The set of optimal policies grows exponentially with the number of objectives, and recovering all solutions requires an exhaustive exploration of the entire state space. We propose Pareto Conditioned Networks (PCN), a method that uses a single neural network to encompass all non-dominated policies. PCN associates every past transition with its episode's return. It trains the network such that, when conditioned on this same return, it should reenact said transition. In doing so we transform the optimization problem into a classification problem. We recover a concrete policy by conditioning the network on the desired Pareto-efficient solution. Our method is stable as it learns in a supervised fashion, thus avoiding moving target issues. Moreover, by using a single network, PCN scales efficiently with the number of objectives. Finally, it makes minimal assumptions on the shape of the Pareto front, which makes it suitable to a wider range of problems than previous state-of-the-art multi-objective RL algorithms.

Pareto Conditioned Networks


We present a Nash equilibrium analysis for single-buyer singleseller multi-unit k-double auctions for scaling-based bidding strategies. We then design a Deep Deterministic Policy Gradient (DDPG) based learning strategy, DDPGBBS, for a participating agent to suggest bids that approximately achieve the above Nash equilibrium. We expand DDPGBBS to be helpful in more complex settings with multiple buyers/sellers trading multiple units in a Periodic Double Auction (PDA), such as the wholesale market in smart-grids. We demonstrate the efficacy of DDPGBBS with Power Trading Agent Competition’s (PowerTAC) wholesale market PDA as a testbed.

Multi-unit Double Auctions: Equilibrium Analysis and Bidding Strategy using DDPG in Smart-grids


The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and mesoscopic traffic modeling - the article introduces a new N-player dynamic routing game with explicit congestion dynamics. The model is well-posed and can reproduce heterogeneous departure times and congestion spill back phenomena. However, as Nash equilibrium computations are PPAD-complete, solving the game becomes intractable for large but realistic numbers of vehicles N. Therefore, the corresponding mean field game is also introduced. Experiments were performed on several classical benchmark networks of the traffic community: the Pigou, Braess, and Sioux Falls networks with heterogeneous origin, destination and departure time tuples. The Pigou and the Braess examples reveal that the mean field approximation is generally very accurate and computationally efficient as soon as the number of vehicles exceeds a few dozen. On the Sioux Falls network (76 links, 100 time steps), this approach enables learning traffic dynamics with more than 14,000 vehicles.

Solving N player dynamic routing games with congestion: a mean field approach


Reconfigurable multi-agent systems consist of a set of autonomous agents, with integrated interaction capabilities that feature oppor tunistic interaction. Agents seemingly reconfigure their interactions interfaces by forming collectives, and interact based on mutual interests. Finding ways to design and analyse the behaviour of these systems is a vigorously pursued research goal. We propose a model checker, named R-CHECK, to allow reasoning about these systems both from an individual- and a system- level. R-CHECK also permits reasoning about interaction protocols and joint missions. R-CHECK supports a high-level input language with symbolic semantics, and provides a modelling convenience for interaction features such as reconfiguration, coalition formation, self-organisation, etc.

R-CHECK: A Model Checker for Verifying Reconfigurable MAS

**Read paper on the following link:**

https://ifaamas.org/Proceedings/aamas2022/pdfs/p1768.pdf

**Abstract:**



On the Complexity of Controlling Amendment and Successive Winners

**Read paper on the following link:**

https://ifaamas.org/Proceedings/aamas2022/pdfs/p1780.pdf

**Abstract:**



A Refined Complexity Analysis of Fair Districting over Graphs

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Three-Dimensional Popular Matching with Cyclic Preferences

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On Achieving Leximin Fairness and Stability in Many-to-One Matchings

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A Refined Complexity Analysis of Fair Districting over Graphs

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Next from AAMAS 2022

Three-Dimensional Popular Matching with Cyclic Preferences

Similar lecture

On Achieving Leximin Fairness and Stability in Many-to-One Matchings

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES

Downloads