Early Pruning for Public Transport Routing

Routing algorithms for public transport, particularly the widely used RAPTOR and its variants, often face performance bottlenecks during the transfer relaxation phase, especially on dense transfer graphs, when supporting unlimited transfers. This inefficiency arises from iterating over many potential inter-stop connections (walks, bikes, e-scooters, etc.). To maintain acceptable performance, practitioners often limit transfer distances or exclude certain transfer options, which can reduce path optimality and restrict the multimodal options presented to travellers. This paper introduces Early Pruning, a low-overhead technique that accelerates routing algorithms without compromising optimality. By pre-sorting transfer connections by duration and applying a pruning rule within the transfer loop, the method discards longer transfers at a stop once they cannot yield an earlier arrival than the current best solution. Early Pruning can be integrated with minimal changes to existing codebases and requires only a one-time preprocessing step. Across multiple state-of-the-art RAPTOR-based solutions, including RAPTOR, ULTRA-RAPTOR, McRAPTOR, BM-RAPTOR, ULTRA-McRAPTOR, and UBM-RAPTOR and tested on the Switzerland and London transit networks, we achieved query time reductions of up to 57%. This approach provides a generalizable improvement to the efficiency of transit pathfinding algorithms. Beyond algorithmic performance, Early Pruning has practical implications for transport planning. By reducing computational costs, it enables transit agencies to expand transfer radii and incorporate additional mobility modes into journey planners without requiring extra server infrastructure. This is particularly relevant for passengers in areas with sparse direct transit coverage, such as outer suburbs and smaller towns, where richer multimodal routing can reveal viable alternatives to private car use.

Adapting Dijkstra for Buffers and Unlimited Transfers

In recent years, RAPTOR based algorithms have been considered the state-of-the-art for path-finding with unlimited transfers without preprocessing. However, this status largely stems from the evolution of routing research, where Dijkstra-based solutions were superseded by timetable-based algorithms without a systematic comparison. In this work, we revisit classical Dijkstra-based approaches for public transit routing with unlimited transfers and demonstrate that Time-Dependent Dijkstra (TD-Dijkstra) outperforms MR. However, efficient TD-Dijkstra implementations rely on filtering dominated connections during preprocessing, which assumes passengers can always switch to a faster connection. We show that this filtering is unsound when stops have buffer times, as it cannot distinguish between seated passengers who may continue without waiting and transferring passengers who must respect the buffer. To address this limitation, we introduce Transfer Aware Dijkstra (TAD), a modification that scans entire trip sequences rather than individual edges, correctly handling buffer times while maintaining performance advantages over MR. Our experiments on London and Switzerland networks show that we can achieve a greater than two time speed-up over MR while producing optimal results on both networks with and without buffer times.

Equitable Mechanism Design for Facility Location

We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarian and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.

Playing games with Large language models: Randomness and strategy

Playing games has a long history of describing intricate interactions in simplified forms. In this paper we explore if large language models (LLMs) can play games, investigating their capabilities for randomisation and strategic adaptation through both simultaneous and sequential game interactions. We focus on GPT-4o-Mini-2024-08-17 and test two games between LLMs: Rock Paper Scissors (RPS) and games of strategy (Prisoners Dilemma PD). LLMs are often described as stochastic parrots, and while they may indeed be parrots, our results suggest that they are not very stochastic in the sense that their outputs - when prompted to be random - are often very biased. Our research reveals that LLMs appear to develop loss aversion strategies in repeated games, with RPS converging to stalemate conditions while PD shows systematic shifts between cooperative and competitive outcomes based on prompt design. We detail programmatic tools for independent agent interactions and the Agentic AI challenges faced in implementation. We show that LLMs can indeed play games, just not very well. These results have implications for the use of LLMs in multi-agent LLM systems and showcase limitations in current approaches to model output for strategic decision-making.

Timetable Nodes for Public Transport Network

Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The solutions that work well in road networks, such as Time-dependent Contraction Hierarchies and other graph-based approaches, do not usually apply in transport networks. In transport networks, non-graph solutions such as CSA and RAPTOR show the best results compared to graph-based techniques. In our work, we propose a method that advances graph-based approaches by using different optimization techniques from computational geometry to speed up the search process in transport networks. We apply a new pre-computation step, which we call timetable nodes (TTN). Our inspiration comes from an iterative search problem in computational geometry. We implement two versions of the TTN: one uses a Combined Search Tree (TTN-CST), and the second uses Fractional Cascading (TTN-FC). Both of these approaches decrease the asymptotic complexity of reaching new nodes from $O(k\times \log|C|)$ to $O(k + \log(k) + \log(|C|))$, where $k$ is the number of outgoing edges from a node and $|C|$ is the size of the timetable information (total outgoing edges). Our solution suits any other time-dependent networks and can be integrated into other pathfinding algorithms. Our experiments indicate that this pre-computation significantly enhances the performance on high-density graphs. This study showcases how leveraging computational geometry can enhance pathfinding in transport networks, enabling faster pathfinding in scenarios involving large numbers of outgoing edges.

Modelling Opaque Bilateral Market Dynamics in Financial Trading: Insights from a Multi-Agent Simulation Study

Exploring complex adaptive financial trading environments through multi-agent based simulation methods presents an innovative approach within the realm of quantitative finance. Despite the dominance of multi-agent reinforcement learning approaches in financial markets with observable data, there exists a set of systematically significant financial markets that pose challenges due to their partial or obscured data availability. We, therefore, devise a multi-agent simulation approach employing small-scale meta-heuristic methods. This approach aims to represent the opaque bilateral market for Australian government bond trading, capturing the bilateral nature of bank-to-bank trading, also referred to as "over-the-counter" (OTC) trading, and commonly occurring between "market makers". The uniqueness of the bilateral market, characterized by negotiated transactions and a limited number of agents, yields valuable insights for agent-based modelling and quantitative finance. The inherent rigidity of this market structure, which is at odds with the global proliferation of multilateral platforms and the decentralization of finance, underscores the unique insights offered by our agent-based model. We explore the implications of market rigidity on market structure and consider the element of stability, in market design. This extends the ongoing discourse on complex financial trading environments, providing an enhanced understanding of their dynamics and implications.

Nash Welfare and Facility Location

We consider the problem of locating a facility to serve a set of agents located along a line. The Nash welfare objective function, defined as the product of the agents' utilities, is known to provide a compromise between fairness and efficiency in resource allocation problems. We apply this welfare notion to the facility location problem, converting individual costs to utilities and analyzing the facility placement that maximizes the Nash welfare. We give a polynomial-time approximation algorithm to compute this facility location, and prove results suggesting that it achieves a good balance of fairness and efficiency. Finally, we take a mechanism design perspective and propose a strategy-proof mechanism with a bounded approximation ratio for Nash welfare.

Mechanisms that play a game, not toss a coin

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such mechanisms by having agents play a game instead of tossing a coin. The game is designed so an agent's best action is to play randomly, and this play then injects ``randomness'' into the mechanism. This derandomization retains many of the good normative properties of the original randomized mechanism but gives a mechanism that is deterministic and easy, for instance, to audit. We consider three related methods to derandomize randomized mechanism in six different domains: voting, facility location, task allocation, school choice, peer selection, and resource allocation. We propose a number of novel derandomized mechanisms for these six domains with good normative properties. Each mechanism has a mixed Nash equilibrium in which agents play a modular arithmetic game with an uniform mixed strategy. In all but one mixed Nash equilibrium, agents report their preferences over the original problem sincerely. The derandomized methods are thus ``quasi-strategy proof''. In one domain, we additionally show that a new and desirable normative property emerges as a result of derandomization.

Incentives to Offer Algorithmic Recourse

Due to the importance of artificial intelligence (AI) in a variety of high-stakes decisions, such as loan approval, job hiring, and criminal bail, researchers in Explainable AI (XAI) have developed algorithms to provide users with recourse for an unfavorable outcome. We analyze the incentives for a decision-maker to offer recourse to a set of applicants. Does the decision-maker have the incentive to offer recourse to all rejected applicants? We show that the decision-maker only offers recourse to all applicants in extreme cases, such as when the recourse process is impossible to manipulate. Some applicants may be worse off when the decision-maker can offer recourse.

Proportional Fairness in Obnoxious Facility Location

We consider the obnoxious facility location problem (in which agents prefer the facility location to be far from them) and propose a hierarchy of distance-based proportional fairness concepts for the problem. These fairness axioms ensure that groups of agents at the same location are guaranteed to be a distance from the facility proportional to their group size. We consider deterministic and randomized mechanisms, and compute tight bounds on the price of proportional fairness. In the deterministic setting, not only are our proportional fairness axioms incompatible with strategyproofness, the Nash equilibria may not guarantee welfare within a constant factor of the optimal welfare. On the other hand, in the randomized setting, we identify proportionally fair and strategyproof mechanisms that give an expected welfare within a constant factor of the optimal welfare.