Physical spaces are increasingly dense with networked devices, promising seamless coordination and ambient intelligence. Yet today, cloud-first architectures force all communication through wide-area networks regardless of physical proximity. We lack an abstraction for spatial networking: using physical spaces to create boundaries for private, robust, and low-latency communication. We introduce $\textit{Bifröst}$, a programming model that realizes spatial networking using bigraphs to express both containment and connectivity, enabling policies to be scoped by physical boundaries, devices to be named by location, the instantiation of spatial services, and the composition of spaces while maintaining local autonomy. Bifröst enables a new class of spatially-aware applications, where co-located devices communicate directly, physical barriers require explicit gateways, and local control bridges to global coordination.

Bigraphical Reactive Systems (BRSs) are a graph-rewriting formalism describing systems evolving in two dimensions: spatially, e.g. a person in a room, and non-spatially, e.g. mobile phones communicating regardless of location. Despite use in domains including communication protocols, agent programming, biology, and security, there is no support for real-time systems. We extend BRSs to support real-time systems with a modelling approach that uses multiple perspectives to represent digital clocks. We use Action BRSs, a recent extension of BRSs, where the resulting transition system is a Markov Decision Process (MDP). This allows a natural representation of the choices in each system state: to either allow time to pass or perform a specific action. We implement our proposed approach using the BigraphER toolkit, and demonstrate the effectiveness through multiple examples including modelling cloud system requests.

Most real-world Multi-Robot Task Allocation (MRTA) problems require fast and efficient decision-making, which is often achieved using heuristics-aided methods such as genetic algorithms, auction-based methods, and bipartite graph matching methods. These methods often assume a form that lends better explainability compared to an end-to-end (learnt) neural network based policy for MRTA. However, deriving suitable heuristics can be tedious, risky and in some cases impractical if problems are too complex. This raises the question: can these heuristics be learned? To this end, this paper particularly develops a Graph Reinforcement Learning (GRL) framework to learn the heuristics or incentives for a bipartite graph matching approach to MRTA. Specifically a Capsule Attention policy model is used to learn how to weight task/robot pairings (edges) in the bipartite graph that connects the set of tasks to the set of robots. The original capsule attention network architecture is fundamentally modified by adding encoding of robots' state graph, and two Multihead Attention based decoders whose output are used to construct a LogNormal distribution matrix from which positive bigraph weights can be drawn. The performance of this new bigraph matching approach augmented with a GRL-derived incentive is found to be at par with the original bigraph matching approach that used expert-specified heuristics, with the former offering notable robustness benefits. During training, the learned incentive policy is found to get initially closer to the expert-specified incentive and then slightly deviate from its trend.

Bigraphical Reactive Systems (BRSs) [14, 20] are a flexible and expressive meta-model for ubiquitous computation. System states are represented by bigraphs, which are compositional data structures describing at once both the locations and the logical connections of (possibly nested) components of a system. Like graph rewriting [25], the dynamic behaviour of a system is defined by a set of (parametric) reaction rules, which can modify a bigraph by replacing a redex with a reactum, possibly changing agents' positions and connections. BRSs have been successfully applied to the formalization of a broad variety of domain-specific calculi and models, from traditional programming languages to process calculi for concurrency and mobility, from context-aware systems to web-service orchestration languages, from business processes to systems biology; a non exhaustive list is [2,4,5,8,16,19]. Very recently bigraphs have been used in structure-aware agent-based computing for modelling the structure of the (physical) world where the agents operates (e.g., drones, robots, etc.) [21]. Beside their normative and expressive power, BRSs are appealing because they provide a range of interesting general results and tools, which can be readily instantiated with the specific model under scrutiny: simulation tools, systematic construction of compositional bisimulations [14], graphical editors [9], general model checkers [24], modular composition [23], stochastic extensions [15], etc. In this paper, we give an implementation for a crucial problem that virtually all these tools have to deal with, i.e., the matching a bigraph inside an agent. Roughly, this can be stated as follows: given R and A, we have to find (all, or some) C,D such that A C R D. Clearly this is required by any simulation tool (in order to apply a reaction rule, we have to match the redex inside the agent, and then replace it with the reactum), but also in other tools, e.g., for implementing "find&replace" in graphical editors, for occurrence checks in sortings [1] and model checkers, for refinements in architectural design tools, etc. 1

Robotic systems, working together as a team, are becoming valuable players in different real-world applications, from disaster response to warehouse fulfillment services. Centralized solutions for coordinating multi-robot teams often suffer from poor scalability and vulnerability to communication disruptions. This paper develops a decentralized multi-agent task allocation (Dec-MATA) algorithm for multi-robot applications. The task planning problem is posed as a maximum-weighted matching of a bipartite graph, the solution of which using the blossom algorithm allows each robot to autonomously identify the optimal sequence of tasks it should undertake. The graph weights are determined based on a soft clustering process, which also plays a problem decomposition role seeking to reduce the complexity of the individual-agents' task assignment problems. To evaluate the new Dec-MATA algorithm, a series of case studies (of varying complexity) are performed, with tasks being distributed randomly over an observable 2D environment. A centralized approach, based on a state-of-the-art MILP formulation of the multi-Traveling Salesman problem is used for comparative analysis. While getting within 7-28% of the optimal cost obtained by the centralized algorithm, the Dec-MATA algorithm is found to be 1-3 orders of magnitude faster and minimally sensitive to task-to-robot ratios, unlike the centralized algorithm.

The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of parameters.We adapt the advances of last decade in unipartite complex networks modeling to the bigraph setting. This data structure can be observed in several situations. However, only a few datasets are freely available to test the algorithms (e.g. community detection, influential nodes identification, information retrieval) which operate on such data. Therefore, artificial datasets are needed to enhance development and testing of the algorithms. We are particularly interested in applying the generator to the analysis of recommender systems. Therefore, we focus on two characteristics that, besides simple statistics, are in our opinion responsible for the performance of neighborhood based collaborative filtering algorithms. The features are node degree distribution and local clustering coeficient.

The purpose of this article is to introduce a new analytical framework dedicated to measuring performance of recommender systems. The standard approach is to assess the quality of a system by means of accuracy related statistics. However, the specificity of the environments in which recommender systems are deployed requires to pay much attention to speed and memory requirements of the algorithms. Unfortunately, it is implausible to assess accurately the complexity of various algorithms with formal tools. This can be attributed to the fact that such analyses are usually based on an assumption of dense representation of underlying data structures. Whereas, in real life the algorithms operate on sparse data and are implemented with collections dedicated for them. Therefore, we propose to measure the complexity of recommender systems with artificial datasets that posses real-life properties. We utilize recently developed bipartite graph generator to evaluate how state-of-the-art recommender systems' behavior is determined and diversified by topological properties of the generated datasets.