Sarvapali D. Ramchurn

Joseph Early, Tom Bewley, Christine Evers et al.

We generalise the problem of reward modelling (RM) for reinforcement learning (RL) to handle non-Markovian rewards. Existing work assumes that human evaluators observe each step in a trajectory independently when providing feedback on agent behaviour. In this work, we remove this assumption, extending RM to capture temporal dependencies in human assessment of trajectories. We show how RM can be approached as a multiple instance learning (MIL) problem, where trajectories are treated as bags with return labels, and steps within the trajectories are instances with unseen reward labels. We go on to develop new MIL models that are able to capture the time dependencies in labelled trajectories. We demonstrate on a range of RL tasks that our novel MIL models can reconstruct reward functions to a high level of accuracy, and can be used to train high-performing agent policies.

David M. Bossens, Sarvapali Ramchurn, Danesh Tarapore

Purpose of review: This paper reviews opportunities and challenges for decentralised control, change-detection, and learning in the context of resilient robot teams. Recent findings: Exogenous fault detection methods can provide a generic detection or a specific diagnosis with a recovery solution. Robot teams can perform active and distributed sensing for detecting changes in the environment, including identifying and tracking dynamic anomalies, as well as collaboratively mapping dynamic environments. Resilient methods for decentralised control have been developed in learning perception-action-communication loops, multi-agent reinforcement learning, embodied evolution, offline evolution with online adaptation, explicit task allocation, and stigmergy in swarm robotics. Summary: Remaining challenges for resilient robot teams are integrating change-detection and trial-and-error learning methods, obtaining reliable performance evaluations under constrained evaluation time, improving the safety of resilient robot teams, theoretical results demonstrating rapid adaptation to given environmental perturbations, and designing realistic and compelling case studies.

Gregory Everett, Ryan J. Beal, Tim Matthews et al.

Understanding agent behaviour in Multi-Agent Systems (MAS) is an important problem in domains such as autonomous driving, disaster response, and sports analytics. Existing MAS problems typically use uniform timesteps with observations for all agents. In this work, we analyse the problem of agent location imputation, specifically posed in environments with non-uniform timesteps and limited agent observability (~95% missing values). Our approach uses Long Short-Term Memory and Graph Neural Network components to learn temporal and inter-agent patterns to predict the location of all agents at every timestep. We apply this to the domain of football (soccer) by imputing the location of all players in a game from sparse event data (e.g., shots and passes). Our model estimates player locations to within ~6.9m; a ~62% reduction in error from the best performing baseline. This approach facilitates downstream analysis tasks such as player physical metrics, player coverage, and team pitch control. Existing solutions to these tasks often require optical tracking data, which is expensive to obtain and only available to elite clubs. By imputing player locations from easy to obtain event data, we increase the accessibility of downstream tasks.

Mohammad Divband Soorati, Enrico H. Gerding, Enrico Marchioni et al.

The Agents, Interaction and Complexity research group at the University of Southampton has a long track record of research in multiagent systems (MAS). We have made substantial scientific contributions across learning in MAS, game-theoretic techniques for coordinating agent systems, and formal methods for representation and reasoning. We highlight key results achieved by the group and elaborate on recent work and open research challenges in developing trustworthy autonomous systems and deploying human-centred AI systems that aim to support societal good.

Joseph Early, Ying-Jung Deweese, Christine Evers et al.

Land cover classification (LCC), and monitoring how land use changes over time, is an important process in climate change mitigation and adaptation. Existing approaches that use machine learning with Earth observation data for LCC rely on fully-annotated and segmented datasets. Creating these datasets requires a large amount of effort, and a lack of suitable datasets has become an obstacle in scaling the use of LCC. In this study, we propose Scene-to-Patch models: an alternative LCC approach utilising Multiple Instance Learning (MIL) that requires only high-level scene labels. This enables much faster development of new datasets whilst still providing segmentation through patch-level predictions, ultimately increasing the accessibility of using LCC for different scenarios. On the DeepGlobe-LCC dataset, our approach outperforms non-MIL baselines on both scene- and patch-level prediction. This work provides the foundation for expanding the use of LCC in climate change mitigation methods for technology, government, and academia.

Oliver Grainge, Michael Milford, Indu Bodala et al.

Visual Place Recognition (VPR) is fundamental for the global re-localization of robots and devices, enabling them to recognize previously visited locations based on visual inputs. This capability is crucial for maintaining accurate mapping and localization over large areas. Given that VPR methods need to operate in real-time on embedded systems, it is critical to optimize these systems for minimal resource consumption. While the most efficient VPR approaches employ standard convolutional backbones with fixed descriptor dimensions, these often lead to redundancy in the embedding space as well as in the network architecture. Our work introduces a novel structured pruning method, to not only streamline common VPR architectures but also to strategically remove redundancies within the feature embedding space. This dual focus significantly enhances the efficiency of the system, reducing both map and model memory requirements and decreasing feature extraction and retrieval latencies. Our approach has reduced memory usage and latency by 21% and 16%, respectively, across models, while minimally impacting recall@1 accuracy by less than 1%. This significant improvement enhances real-time applications on edge devices with negligible accuracy loss.

Shuang Ao, Yi Dong, Jinwei Hu et al.

Fine-tuning Large Language Models (LLMs) with Low-Rank Adaptation (LoRA) enhances adaptability while reducing computational costs. However, fine-tuning can compromise safety alignment, even with benign data, increasing susceptibility to harmful outputs. Existing safety alignment methods struggle to capture complex parameter shifts, leading to suboptimal safety-utility trade-offs. To address this issue, we propose Safe Pruning LoRA (SPLoRA), a novel pruning-based approach that selectively removes LoRA layers that weaken safety alignment, improving safety while preserving performance. At its core, we introduce Empirical-DIEM (E-DIEM), a dimension-insensitive similarity metric that effectively detects safety misalignment in LoRA-adapted models. We conduct extensive experiments on LLMs fine-tuned with mixed of benign and malicious data, and purely benign datasets, evaluating SPLoRA across utility, safety, and reliability metrics. Results demonstrate that SPLoRA outperforms state-of-the-art safety alignment techniques, significantly reducing safety risks while maintaining or improving model performance and reliability. Additionally, SPLoRA reduces inference overhead, making it a scalable and efficient solution for deploying safer and more reliable LLMs. The code is available at https://github.com/AoShuang92/SPLoRA.

Jinwei Hu, Yi Dong, Shuang Ao et al.

The rise of Agent AI and Large Language Model-powered Multi-Agent Systems (LLM-MAS) has underscored the need for responsible and dependable system operation. Tools like LangChain and Retrieval-Augmented Generation have expanded LLM capabilities, enabling deeper integration into MAS through enhanced knowledge retrieval and reasoning. However, these advancements introduce critical challenges: LLM agents exhibit inherent unpredictability, and uncertainties in their outputs can compound across interactions, threatening system stability. To address these risks, a human-centered design approach with active dynamic moderation is essential. Such an approach enhances traditional passive oversight by facilitating coherent inter-agent communication and effective system governance, allowing MAS to achieve desired outcomes more efficiently.

Oliver Grainge, Michael Milford, Indu Bodala et al.

Visual Place Recognition (VPR) is a critical task for performing global re-localization in visual perception systems. It requires the ability to accurately recognize a previously visited location under variations such as illumination, occlusion, appearance and viewpoint. In the case of robotic systems and augmented reality, the target devices for deployment are battery powered edge devices. Therefore whilst the accuracy of VPR methods is important so too is memory consumption and latency. Recently new works have focused on the recall@1 metric as a performance measure with limited focus on resource utilization. This has resulted in methods that use deep learning models too large to deploy on low powered edge devices. We hypothesize that these large models are highly over-parameterized and can be optimized to satisfy the constraints of a low powered embedded system whilst maintaining high recall performance. Our work studies the impact of compact convolutional network architecture design in combination with full-precision and mixed-precision post-training quantization on VPR performance. Importantly we not only measure performance via the recall@1 score but also measure memory consumption and latency. We characterize the design implications on memory, latency and recall scores and provide a number of design recommendations for VPR systems under these resource limitations.

Sania Waheed, Bruno Ferrarini, Michael Milford et al.

The advances in Vision-Language models (VLMs) offer exciting opportunities for robotic applications involving image geo-localization, the problem of identifying the geo-coordinates of a place based on visual data only. Recent research works have focused on using a VLM as embeddings extractor for geo-localization, however, the most sophisticated VLMs may only be available as black boxes that are accessible through an API, and come with a number of limitations: there is no access to training data, model features and gradients; retraining is not possible; the number of predictions may be limited by the API; training on model outputs is often prohibited; and queries are open-ended. The utilization of a VLM as a stand-alone, zero-shot geo-localization system using a single text-based prompt is largely unexplored. To bridge this gap, this paper undertakes the first systematic study, to the best of our knowledge, to investigate the potential of some of the state-of-the-art VLMs as stand-alone, zero-shot geo-localization systems in a black-box setting with realistic constraints. We consider three main scenarios for this thorough investigation: a) fixed text-based prompt; b) semantically-equivalent text-based prompts; and c) semantically-equivalent query images. We also take into account the auto-regressive and probabilistic generation process of the VLMs when investigating their utility for geo-localization task by using model consistency as a metric in addition to traditional accuracy. Our work provides new insights in the capabilities of different VLMs for the above-mentioned scenarios.

Gregory Everett, Ryan Beal, Tim Matthews et al.

In this paper, we present a novel sequential team selection model in soccer. Specifically, we model the stochastic process of player injury and unavailability using player-specific information learned from real-world soccer data. Monte-Carlo Tree Search is used to select teams for games that optimise long-term team performance across a soccer season by reasoning over player injury probability. We validate our approach compared to benchmark solutions for the 2018/19 English Premier League season. Our model achieves similar season expected points to the benchmark whilst reducing first-team injuries by ~13% and the money inefficiently spent on injured players by ~11% - demonstrating the potential to reduce costs and improve player welfare in real-world soccer teams.

Timur Ismagilov, Shakaiba Majeed, Michael Milford et al.

We address multi-reference visual place recognition (VPR), where reference sets captured under varying conditions are used to improve localisation performance. While deep learning with large-scale training improves robustness, increasing data diversity and model complexity incur extensive computational cost during training and deployment. Descriptor-level fusion via voting or aggregation avoids training, but often targets multi-sensor setups or relies on heuristics with limited gains under appearance and viewpoint change. We propose a training-free, descriptor-agnostic approach that jointly models places using multiple reference descriptors via matrix decomposition into basis representations, enabling projection-based residual matching. We also introduce SotonMV, a structured benchmark for multi-viewpoint VPR. On multi-appearance data, our method improves Recall@1 by up to ~18% over single-reference and outperforms multi-reference baselines across appearance and viewpoint changes, with gains of ~5% on unstructured data, demonstrating strong generalisation while remaining lightweight.

Aleksandra Landowska, Aislinn D Gomez Bergin, Ayodeji O. Abioye et al.

This paper introduces and overviews a multidisciplinary project aimed at developing responsible and adaptive multi-human multi-robot (MHMR) systems for complex, dynamic settings. The project integrates co-design, ethical frameworks, and multimodal sensing to create AI-driven robots that are emotionally responsive, context-aware, and aligned with the needs of diverse users. We outline the project's vision, methodology, and early outcomes, demonstrating how embodied AI can support sustainable, ethical, and human-centred futures.

Sania Waheed, Na Min An, Michael Milford et al.

Geo-localization from a single image at planet scale (essentially an advanced or extreme version of the kidnapped robot problem) is a fundamental and challenging task in applications such as navigation, autonomous driving and disaster response due to the vast diversity of locations, environmental conditions, and scene variations. Traditional retrieval-based methods for geo-localization struggle with scalability and perceptual aliasing, while classification-based approaches lack generalization and require extensive training data. Recent advances in vision-language models (VLMs) offer a promising alternative by leveraging contextual understanding and reasoning. However, while VLMs achieve high accuracy, they are often prone to hallucinations and lack interpretability, making them unreliable as standalone solutions. In this work, we propose a novel hybrid geo-localization framework that combines the strengths of VLMs with retrieval-based visual place recognition (VPR) methods. Our approach first leverages a VLM to generate a prior, effectively guiding and constraining the retrieval search space. We then employ a retrieval step, followed by a re-ranking mechanism that selects the most geographically plausible matches based on feature similarity and proximity to the initially estimated coordinates. We evaluate our approach on multiple geo-localization benchmarks and show that it consistently outperforms prior state-of-the-art methods, particularly at street (up to 4.51%) and city level (up to 13.52%). Our results demonstrate that VLM-generated geographic priors in combination with VPR lead to scalable, robust, and accurate geo-localization systems.

Oliver Grainge, Michael Milford, Indu Bodala et al.

TAT-VPR is a ternary-quantized transformer that brings dynamic accuracy-efficiency trade-offs to visual SLAM loop-closure. By fusing ternary weights with a learned activation-sparsity gate, the model can control computation by up to 40% at run-time without degrading performance (Recall@1). The proposed two-stage distillation pipeline preserves descriptor quality, letting it run on micro-UAV and embedded SLAM stacks while matching state-of-the-art localization accuracy.

Oliver Grainge, Michael Milford, Indu Bodala et al.

Visual Place Recognition (VPR) localizes a query image by matching it against a database of geo-tagged reference images, making it essential for navigation and mapping in robotics. Although Vision Transformer (ViT) solutions deliver high accuracy, their large models often exceed the memory and compute budgets of resource-constrained platforms such as drones and mobile robots. To address this issue, we propose TeTRA, a ternary transformer approach that progressively quantizes the ViT backbone to 2-bit precision and binarizes its final embedding layer, offering substantial reductions in model size and latency. A carefully designed progressive distillation strategy preserves the representational power of a full-precision teacher, allowing TeTRA to retain or even surpass the accuracy of uncompressed convolutional counterparts, despite using fewer resources. Experiments on standard VPR benchmarks demonstrate that TeTRA reduces memory consumption by up to 69% compared to efficient baselines, while lowering inference latency by 35%, with either no loss or a slight improvement in recall@1. These gains enable high-accuracy VPR on power-constrained, memory-limited robotic platforms, making TeTRA an appealing solution for real-world deployment.

Matthew Wear, Ryan Beal, Tim Matthews et al.

As an amateur goalkeeper playing grassroots soccer, who better to learn from than top professional goalkeepers? In this paper, we harness computer vision and machine learning models to appraise the save technique of professionals in a way those at lower levels can learn from. We train an unsupervised machine learning model using 3D body pose data extracted from broadcast footage to learn professional goalkeeper technique. Then, an "expected saves" model is developed, from which we can identify the optimal goalkeeper technique in different match contexts.

Mohammad Naiseh, Caitlin Bentley, Sarvapali D. Ramchurn

Recent advances in artificial intelligence, specifically machine learning, contributed positively to enhancing the autonomous systems industry, along with introducing social, technical, legal and ethical challenges to make them trustworthy. Although Trustworthy Autonomous Systems (TAS) is an established and growing research direction that has been discussed in multiple disciplines, e.g., Artificial Intelligence, Human-Computer Interaction, Law, and Psychology. The impact of TAS on education curricula and required skills for future TAS engineers has rarely been discussed in the literature. This study brings together the collective insights from a number of TAS leading experts to highlight significant challenges for curriculum design and potential TAS required skills posed by the rapid emergence of TAS. Our analysis is of interest not only to the TAS education community but also to other researchers, as it offers ways to guide future research toward operationalising TAS education.

Joseph Early, Christine Evers, Sarvapali Ramchurn

In Multiple Instance Learning (MIL), models are trained using bags of instances, where only a single label is provided for each bag. A bag label is often only determined by a handful of key instances within a bag, making it difficult to interpret what information a classifier is using to make decisions. In this work, we establish the key requirements for interpreting MIL models. We then go on to develop several model-agnostic approaches that meet these requirements. Our methods are compared against existing inherently interpretable MIL models on several datasets, and achieve an increase in interpretability accuracy of up to 30%. We also examine the ability of the methods to identify interactions between instances and scale to larger datasets, improving their applicability to real-world problems.

Luca Capezzuto, Danesh Tarapore, Sarvapali D. Ramchurn

The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP) is a multi-agent task allocation problem in which few agents have to perform many tasks, each with its deadline and workload. To maximize the number of completed tasks, the agents need to cooperate by forming, disbanding and reforming coalitions. The original mathematical programming formulation of the CFSTP is difficult to implement, since it is lengthy and based on the problematic Big-M method. In this paper, we propose a compact and easy-to-implement formulation. Moreover, we design D-CTS, a distributed version of the state-of-the-art CFSTP algorithm. Using public London Fire Brigade records, we create a dataset with $347588$ tasks and a test framework that simulates the mobilization of firefighters in dynamic environments. In problems with up to $150$ agents and $3000$ tasks, compared to DSA-SDP, a state-of-the-art distributed algorithm, D-CTS completes $3.79\% \pm [42.22\%, 1.96\%]$ more tasks, and is one order of magnitude more efficient in terms of communication overhead and time complexity. D-CTS sets the first large-scale, dynamic and distributed CFSTP benchmark.

Luca Capezzuto, Danesh Tarapore, Sarvapali D. Ramchurn

In task allocation for real-time domains, such as disaster response, a limited number of agents is deployed across a large area to carry out numerous tasks, each with its prerequisites, profit, time window and workload. To maximize profits while minimizing time penalties, agents need to cooperate by forming, disbanding and reforming coalitions. In this paper, we name this problem Multi-Agent Routing and Scheduling through Coalition formation (MARSC) and show that it generalizes the important Team Orienteering Problem with Time Windows. We propose a binary integer program and an anytime and scalable heuristic to solve it. Using public London Fire Brigade records, we create a dataset with 347588 tasks and a test framework that simulates the mobilization of firefighters. In problems with up to 150 agents and 3000 tasks, our heuristic finds solutions up to 3.25 times better than the Earliest Deadline First approach commonly used in real-time systems. Our results constitute the first large-scale benchmark for the MARSC problem.

Ryan Beal, Georgios Chalkiadakis, Timothy J. Norman et al.

In this paper, we present a novel approach for optimising long-term tactical and strategic decision-making in football (soccer) by encapsulating events in a league environment across a given time frame. We model the teams' objectives for a season and track how these evolve as games unfold to give a fluent objective that can aid in decision-making games. We develop Markov chain Monte Carlo and deep learning-based algorithms that make use of the fluent objectives in order to learn from prior games and other games in the environment and increase the teams' long-term performance. Simulations of our approach using real-world datasets from 760 matches shows that by using optimised tactics with our fluent objective and prior games, we can on average increase teams mean expected finishing distribution in the league by up to 35.6%.

Ryan Beal, Stuart E. Middleton, Timothy J. Norman et al.

In this paper, we present a new application-focused benchmark dataset and results from a set of baseline Natural Language Processing and Machine Learning models for prediction of match outcomes for games of football (soccer). By doing so we give a baseline for the prediction accuracy that can be achieved exploiting both statistical match data and contextual articles from human sports journalists. Our dataset is focuses on a representative time-period over 6 seasons of the English Premier League, and includes newspaper match previews from The Guardian. The models presented in this paper achieve an accuracy of 63.18% showing a 6.9% boost on the traditional statistical methods.

Luca Capezzuto, Danesh Tarapore, Sarvapali D. Ramchurn

The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP) is a multi-agent task scheduling problem where the tasks are spatially distributed, with deadlines and workloads, and the number of agents is typically much smaller than the number of tasks, thus the agents have to form coalitions in order to maximise the number of completed tasks. The current state-of-the-art CFSTP solver, the Coalition Formation with Look-Ahead (CFLA) algorithm, has two main limitations. First, its time complexity is exponential with the number of agents. Second, as we show, its look-ahead technique is not effective in real-world scenarios, such as open multi-agent systems, where new tasks can appear at any time. In this work, we study its design and define an extension, called Coalition Formation with Improved Look-Ahead (CFLA2), which achieves better performance. Since we cannot eliminate the limitations of CFLA in CFLA2, we also develop a novel algorithm to solve the CFSTP, the first to be anytime, efficient and with provable guarantees, called Cluster-based Coalition Formation (CCF). We empirically show that, in settings where the look-ahead technique is highly effective, CCF completes up to 30% (resp. 10%) more tasks than CFLA (resp. CFLA2) while being up to four orders of magnitude faster. Our results affirm CCF as the new state-of-the-art algorithm to solve the CFSTP.

Ryan Beal, Georgios Chalkiadakis, Timothy J. Norman et al.

In this paper we present a novel approach to optimise tactical and strategic decision making in football (soccer). We model the game of football as a multi-stage game which is made up from a Bayesian game to model the pre-match decisions and a stochastic game to model the in-match state transitions and decisions. Using this formulation, we propose a method to predict the probability of game outcomes and the payoffs of team actions. Building upon this, we develop algorithms to optimise team formation and in-game tactics with different objectives. Empirical evaluation of our approach on real-world datasets from 760 matches shows that by using optimised tactics from our Bayesian and stochastic games, we can increase a team chances of winning by up to 16.1\% and 3.4\% respectively.

Filippo Bistaffa, Alessandro Farinelli, Jesús Cerquides et al.

Coalition formation typically involves the coming together of multiple, heterogeneous, agents to achieve both their individual and collective goals. In this paper, we focus on a special case of coalition formation known as Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. We propose a novel representation of this problem based on the concept of edge contraction, which allows us to model the search space induced by the GCCF problem as a rooted tree. Then, we propose an anytime solution algorithm (CFSS), which is particularly efficient when applied to a general class of characteristic functions called $m+a$ functions. Moreover, we show how CFSS can be efficiently parallelised to solve GCCF using a non-redundant partition of the search space. We benchmark CFSS on both synthetic and realistic scenarios, using a real-world dataset consisting of the energy consumption of a large number of households in the UK. Our results show that, in the best case, the serial version of CFSS is 4 orders of magnitude faster than the state of the art, while the parallel version is 9.44 times faster than the serial version on a 12-core machine. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems of agents (i.e., with more than 2700 agents).

Dengji Zhao, Sarvapali D. Ramchurn, Nicholas R. Jennings

We study a general task allocation problem, involving multiple agents that collaboratively accomplish tasks and where agents may fail to successfully complete the tasks assigned to them (known as execution uncertainty). The goal is to choose an allocation that maximises social welfare while taking their execution uncertainty into account. We show that this can be achieved by using the post-execution verification (PEV)-based mechanism if and only if agents' valuations satisfy a multilinearity condition. We then consider a more complex setting where an agent's execution uncertainty is not completely predictable by the agent alone but aggregated from all agents' private opinions (known as trust). We show that PEV-based mechanism with trust is still truthfully implementable if and only if the trust aggregation is multilinear.

Talal Rahwan, Sarvapali Dyanand Ramchurn, Nicholas Robert Jennings et al.

Coalition formation is a fundamental type of interaction that involves the creation of coherent groupings of distinct, autonomous, agents in order to efficiently achieve their individual or collective goals. Forming effective coalitions is a major research challenge in the field of multi-agent systems. Central to this endeavour is the problem of determining which of the many possible coalitions to form in order to achieve some goal. This usually requires calculating a value for every possible coalition, known as the coalition value, which indicates how beneficial that coalition would be if it was formed. Once these values are calculated, the agents usually need to find a combination of coalitions, in which every agent belongs to exactly one coalition, and by which the overall outcome of the system is maximized. However, this coalition structure generation problem is extremely challenging due to the number of possible solutions that need to be examined, which grows exponentially with the number of agents involved. To date, therefore, many algorithms have been proposed to solve this problem using different techniques ranging from dynamic programming, to integer programming, to stochastic search all of which suffer from major limitations relating to execution time, solution quality, and memory requirements. With this in mind, we develop an anytime algorithm to solve the coalition structure generation problem. Specifically, the algorithm uses a novel representation of the search space, which partitions the space of possible solutions into sub-spaces such that it is possible to compute upper and lower bounds on the values of the best coalition structures in them. These bounds are then used to identify the sub-spaces that have no potential of containing the optimal solution so that they can be pruned. The algorithm, then, searches through the remaining sub-spaces very efficiently using a branch-and-bound technique to avoid examining all the solutions within the searched subspace(s). In this setting, we prove that our algorithm enumerates all coalition structures efficiently by avoiding redundant and invalid solutions automatically. Moreover, in order to effectively test our algorithm we develop a new type of input distribution which allows us to generate more reliable benchmarks compared to the input distributions previously used in the field. Given this new distribution, we show that for 27 agents our algorithm is able to find solutions that are optimal in 0.175% of the time required by the fastest available algorithm in the literature. The algorithm is anytime, and if interrupted before it would have normally terminated, it can still provide a solution that is guaranteed to be within a bound from the optimal one. Moreover, the guarantees we provide on the quality of the solution are significantly better than those provided by the previous state of the art algorithms designed for this purpose. For example, for the worst case distribution given 25 agents, our algorithm is able to find a 90% efficient solution in around 10% of time it takes to find the optimal solution.