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We study multi-task reinforcement learning (RL), a setting in which an agent learns a single, universal policy capable of generalising to arbitrary, possibly unseen tasks. We consider tasks specified as linear temporal logic (LTL) formulae, which are commonly used in formal methods to specify properties of systems, and have recently been successfully adopted in RL. In this setting, we present a novel task embedding technique leveraging a new generation of semantic LTL-to-automata translations, originally developed for temporal synthesis. The resulting semantically labelled automata contain rich, structured information in each state that allow us to (i) compute the automaton efficiently on-the-fly, (ii) extract expressive task embeddings used to condition the policy, and (iii) naturally support full LTL. Experimental results in a variety of domains demonstrate that our approach achieves state-of-the-art performance and is able to scale to complex specifications where existing methods fail.
Achieving optimal coordination in multiagent systems involves a trade-off between intractable centralized planning and suboptimal decentralized execution. We bridge this gap by introducing Approximate Recursive Small Step-Semi-Decentralized A* (RS-SDA*), a tree search algorithm that exploits time-varying centralization during periods of available communication conditioned on the environment or joint actions. By interleaving offline planning with online search and using relaxed heuristics, RS-SDA* achieves high solution quality with reduced computational overhead. SDec-POMDP benchmark experiments show that Approximate RS-SDA* often finds near exact optimal solutions in less than 1% of the time required by exact algorithms. We show scalability in six labyrinth environments both deterministic and stochastic state transitions, and demonstrate real-world feasibility with a multi-drone search-and-rescue simulation in the DARPA Subterranean Challenge cave system.
In several socioeconomic-critical decision-making settings, such as fair resource allocation, climate policy, or AI alignment, multiple principals interact within a common arena. While it is well established that these principals may have differing preferences, decision-making under heterogeneous time preferences remains relatively unexplored. In particular, principals may weigh future outcomes differently and may derive distinct utilities from the same decisions. Motivated by such scenarios, we introduce the notion of heterogeneous time preferences in MDPs, where multiple principals possess distinct reward functions and apply different discount factors to future rewards. To compute meaningful decisions in such settings, an AI agent must rely on a notion of optimality that accounts for the preferences of all principals. We adopt a utilitarian notion of social welfare, defined as the sum of utilities accrued to all principals, and study the synthesis of agent strategies that maximise this welfare. Under heterogeneous time preferences, we show that optimal strategies are no longer positional, even when all principals receive identical rewards. Nevertheless, optimal strategies remain structurally simple: they can be realised as pure finite-memory counting strategies, require only polynomial memory in the system size, and can be synthesised in polynomial time. On the other hand, we show that deciding threshold questions for optimal positional strategies is NP-hard, exposing a poor trade-off: insisting on positional simplicity neither makes synthesis tractable nor preserves social welfare.
Strategy synthesis typically follows an all-or-nothing paradigm, returning unrealisable whenever a specification cannot be guaranteed in an uncertain environment. In this paper, we introduce optimal LTLf synthesis, where the goal is to realise as many objectives as possible from a given specification consisting of multiple objectives, especially for the case that they are not all jointly realisable. We first consider max-guarantee synthesis, which commits to a maximal set of objectives that we can a priori guarantee to realise. We then introduce max-observation synthesis, which maximises a posteriori realised objectives that may be incomparable on different executions. Finally, we present incremental max-observation synthesis, which further improves strategies by exploiting opportunities for stronger guarantees when they arise during an execution. Experimental results show that different variations of optimal synthesis scale broadly equally well, solving a large fraction of the benchmark instances within the given timeout, demonstrating the practical feasibility of the approach.
Hedonic games are a central model of coalition formation, yet most of their general subclasses are marked by negative results: stable outcomes often fail to exist, and deciding their existence is typically computationally hard. The most notable exception is the class of hedonic games with the common ranking property (HGCRP), a nontrivial subclass that guarantees both the existence and tractability of stable partitions. The common ranking property implies the top-coalition property, which in turn implies the weak top-coalition property, forming a natural hierarchy of increasingly general domains. In this paper, we extend the frontier of strong existence and tractability results beyond the HGCRP to hedonic games with the top-coalition property (HGTCP) and hedonic games with the weak top-coalition property (HGWTCP). We show that every HGWTCP instance admits a strong individually stable (SIS) partition that can be computed in polynomial time, and prove that our polynomial-time algorithm generates a partition that is both SIS and Pareto optimal (PO) if preferences are strict. These results show that strong stability and tractability results persist well beyond the common ranking framework. We further show that a contractually Nash stable (CNS) partition may fail to exist even in HGTCP, revealing a sharp contrast with HGCRP, where the existence of partitions that are both CNS and PO is guaranteed. Taken together, these results provide a comprehensive characterization of stability and efficiency in top-coalition-based hedonic games, mapping how stability guarantees evolve from HGCRP to HGWTCP.
Reachability games are two-player games played on a graph, where the objective of REACH player is to reach the target set whereas the objective of SAFE player is to stay away from the target set. Reachability games have important applications in artificial intelligence and reactive synthesis, and many of these applications give rise to infinite-state reachability games. In this paper, we study turn-based reachability games on infinite-state graphs defined over valuations of a finite set of real variables. We consider the problem of determining the existence of and computing a winning strategy for REACH player. Our contributions are twofold. First, we propose ranking certificates for reachability games, a sound and complete proof rule for proving that REACH player has a winning strategy from the specified initial state. Second, we consider polynomial reachability games, where transitions and objectives are described by polynomial constraints over real variables, and propose a fully automated algorithm for computing a winning strategy for REACH player together with a formal correctness witness in the form of a ranking certificate. The algorithm is sound, semi-complete, and runs in sub-exponential time. Our experiments demonstrate the ability of our method to solve challenging examples from the literature that were out of the reach of existing methods. Specifically, for the classical Cinderella-Stepmother game, we are able to compute an optimal winning strategy for an arbitrary precision parameter for the first time.
Unmanned aerial vehicle swarms in pursuit-evasion requires encirclement efficiency while maintaining safety constraints, facing a critical safety-efficiency trade-off. Existing safe multi-agent reinforcement learning (MARL) methods often yield either unsafe task policies or conservative policies. This is challenging since forward feasible safety under dense interactions requires online safety preview. To address this issue, we propose Safety-Constrained Online Preview Enforcement (SCOPE), a MARL-based algorithm that balances encirclement efficiency and safety by short-horizon preview and safety enforcement. SCOPE learns an online safety-preview dynamics model that rolls out future trajectories to inform encirclement decisions checking. By proposing preview-fused actor-critic, SCOPE uses short-horizon previews for efficient encirclement and less unsafe behavior. Hierarchical safety enforcement performs safety look-ahead and online action correction to maintain forward feasible safety. Experiments show that SCOPE better balances encirclement efficiency and safety than safe MARL baselines, maintaining average encirclement time while reducing the average agent cost by 65.6%. Code could be found at https://github.com/98177qdn/SCOPE.
We study the problem of optimally placing charging stations for a set of k anonymous mobile agents, each of which must reach a distinct terminal. The agents are identical and can travel only up to a given distance r on a single charge. The objective is to find a placement of charging stations so that every terminal can be assigned a unique agent capable of reaching it, and the number of charging stations is minimized. The problem is known to be NP-hard in general and solvable in polynomial time only on paths and cycles. In this work, we comprehensively investigate the classical and parameterized complexity of the problem. We first design a polynomial-time algorithm that, given a set of candidate charging stations, decides whether a feasible assignment of agents to terminals exists. This result also establishes the membership of the problem in NP, which was not previously known. We then analyze the parameterized complexity of the problem. Our results show that the problem remains hard even when we consider different combinations of natural parameters and structural parameters of the given network, such as the distance r plus the tree-depth, or the number of charging stations plus feedback vertex set number. On the positive side, we present three fixed-parameter tractable (FPT) algorithms: one parameterized by the number of agents k, a second by modular-width, and a third by vertex cover number. Finally, we give a polynomial-time k-approximation algorithm, as well as a polynomial-time algorithm for trees, by solving a generalized version of the problem that allows for some charging stations to be pre-placed.
TD(λ) in value-based MARL algorithms or the Temporal Difference critic learning in Actor-Critic-based (AC-based) algorithms synergistically integrate elements from Monte-Carlo simulation and Q function bootstrapping via dynamic programming, which effectively addresses the inherent bias-variance trade-off in value estimation. Based on that, some recent works link the adaptive λ value to the policy distribution in the single-agent reinforcement learning area. However, because of the large joint action space from multiple agents and the limited transition data in Multi-agent Reinforcement Learning, the policy distribution is infeasible to calculate statistically. To solve the policy distribution calculation problem in MARL settings, we employ a parametric likelihood-free density ratio estimator with two replay buffers instead of calculating statistically. The two replay buffers of different sizes respectively store the historical trajectories that represent the data distribution of the past and current policies. Based on the estimator, we assign Adaptive TD(λ), ATD(λ), values to state-action pairs based on their likelihood under the stationary distribution of the current policy. We apply the proposed method on two competitive baseline methods, QMIX for value-based algorithms, and MAPPO for AC-based algorithms, over SMAC benchmarks and Gfootball academy scenarios, and demonstrate consistently competitive or superior performance compared to other baseline approaches with static λ values.
Current self-evolution methods mostly chase recall, they learn from any trajectory that ends with the right answer, even when the path relies on a "lucky guess". Such reasoning appears valid in-distribution but often fails the moment the task shifts slightly. We argue that robust evolution implies Structural Invariance: a reasoning path is valid only if its core dependency graph remains isomorphic under counterfactual perturbations. I-EDI enforces this with Verifiable Counterfactual Simulation (VCS). Instead of treating data generation as mere "sample and filter," we treat it as an intervention. Unlike standard rejection sampling, VCS acts as a structural stress test: it accepts a reasoning trace only if it remains valid across generated counterfactuals (e.g., numerical perturbations, context shifts). While this strict filtering reduces the volume of training data (trading recall for precision), our experiments on MATH and GSM8K show it effectively prevents hallucination accumulation, achieving superior out-of-distribution generalization compared to baselines.
Recent advances in large language models (LLMs) allow agents to represent actions as executable code, offering greater expressivity than traditional tool-calling. However, real-world tasks often demand both strategic planning and detailed implementation. Using a single agent for both leads to context pollution from debugging traces and intermediate failures, impairing long-horizon performance. We propose CodeDelegator, a multi-agent framework that separates planning from implementation via role specialization. A persistent Delegator maintains strategic oversight by decomposing tasks, writing specifications, and monitoring progress without executing code. For each sub-task, a new Coder agent is instantiated with a clean context containing only its specification, shielding it from prior failures. To coordinate between agents, we introduce Ephemeral-Persistent State Separation (EPSS), which isolates each Coder's execution state while preserving global coherence, preventing debugging traces from polluting the Delegator's context. Experiments on various benchmarks demonstrate the effectiveness of CodeDelegator across diverse scenarios. Code is available at https://github.com/txfei/code-delegator.
Dynamic systems in AI are often complex and heterogeneous, so that an internal specification is not accessible and hence verification techniques like model checking are not applicable. Monitoring is in such cases an attractive alternative, as it deals with the observation of desirable properties along traces generated by an unknown dynamic system. In this work, we consider anticipatory monitoring of linear-time properties enriched with an arbitrary SMT theory over finite traces (data-LTLf). Anticipatory monitoring in this setting is a highly challenging problem and undecidable in general, as the monitoring state depends on both the trace prefix seen so far and all its possible finite continuations. Under reasonable assumptions on the background theory, we present and formally prove the correctness of a novel foundational framework for monitoring data-LTLf properties. The framework combines automata-theoretic methods to handle the temporal aspects of reasoning with automated reasoning techniques to address the first-order dimension. Moreover, we identify for the first time decidable fragments of this monitoring problem that are practically relevant as they combine linear arithmetic with uninterpreted functions, which covers e.g. data-aware business processes and dynamic systems operating over a database. Feasibility is witnessed by a prototype implementation and preliminary evaluation.
Transformer models are rapidly becoming a cornerstone of modern Internet of Things (IoT) applications, yet their computational and memory demands far exceed the capabilities of a single typical ultra-low-power IoT device. We present CATS, a framework for distributed transformer inference on ultra-low-power wireless devices, enabling multiple devices to collaboratively execute models far larger than what a single device can sustain. At its core, CATS is a communication-aware distributed transformer inference scheme co-designed across transformer partitioning, wireless communication and training. It employs SomeGather, a new pruned communication primitive that selectively broadcasts activation columns to reduce communication bandwidth and RAM usage without sacrificing model accuracy. Building on SomeGather, we design a partitioning method that exploits this primitive for efficient model parallelism. To cope with unreliable wireless communication, CATS employs message-dropout during training, which mimics packet losses and yields models that are robust to message loss during inference. In real-world experiments, we show that CATS brings distributed transformer inference to ultra-low-power wireless devices for the first time, with deployments on up to 16 devices that collaboratively execute transformer models up to 14 times larger than what a single device can run.
Empowered by large language models (LLMs), multi-agent systems (MAS) have shown significant potential in code generation by simulating collaborative workflows. However, we identify a collaboration degeneration phenomenon, where one agent dominates while others remain disengaged, occurring in 38.4% of non-routine HumanEval tasks. Surprisingly, introducing competition among LLM agents eliminates this degeneration and sparks innovation in generated code. Inspired by this catfish effect, we posit that competition helps prevent collaboration degeneration. We thus propose C3, a Controllable Competitive Collaboration framework featuring two novel mechanisms: Centralized Auction-Based Competition (CAB) for role allocation via bidding and Decentralized Communication-Aware Competition (DCC) for solution refinement through opponent-aware adaptation. Evaluated on 70 complex projects from extended SoftwareDev, C3 reduces collaboration degeneration from 32.4% to 12.8%, while enhancing code innovation and diversity. Human evaluations further confirm C3’s superiority in functionality, maintainability, and robustness over purely collaborative or competitive baselines.
Tool learning methods have enhanced the ability of large language models (LLMs) to interact with real-world applications. Many existing works fine-tune LLMs or design prompts to enable LLMs to select appropriate tools and correctly invoke them to meet user requirements. However, it is observed in previous works that the performance of tool learning varies from tasks, datasets, training settings, and algorithms. Without understanding the impact of these factors, it can lead to inconsistent results, inefficient model deployment, and suboptimal tool utilization, ultimately hindering the practical integration and scalability of LLMs in real-world scenarios. Therefore, in this paper, we explore the impact of both internal and external factors on the performance of tool learning frameworks. Through extensive experiments on two benchmark datasets, we find several insightful conclusions for future work, including the observation that LLMs can benefit significantly from increased trial and exploration. We believe our empirical study provides a new perspective for future tool learning research.
Clinical Computed Tomography (CT) reconstruction often faces mixed degradations, where quantum noise, streak artifacts, and geometric distortions co-occur with various compositions and severities. Recently, all-in-one frameworks have outperformed traditional single-task models through degradation-specialized modulation mechanisms. However, attempting to resolve these mixed degradations simultaneously forces the model into suboptimal trade-offs, failing to balance conflicting reconstruction objectives. Our empirical study shows that decomposing CT reconstruction into a sequence of ordered steps effectively mitigates this conflict, with the execution order being a critical performance factor. Leveraging this insight, we propose AgenticCT, an LLM-orchestrated multi-agent framework designed to autonomously plan the optimal reconstruction trajectory. Specifically, AgenticCT operates through a diagnose-plan-treat workflow: a Supervisor Agent explicitly estimates a structured degradation state; a Planner Agent then selects a topology-optimized execution order conditioned on this state; and a library of Processor Agents sequentially executes the trajectory to achieve high-fidelity reconstruction. Extensive experiments demonstrate that AgenticCT consistently improves reconstruction fidelity across single and mixed degradations, and generalizes better to out-of-distribution datasets compared with strong specialized and all-in-one baselines. Code is available at: https://github.com/yqhuang2912/AgenticCT.
We study EFX and approximate EFX allocations of indivisible goods among agents with at most k distinct valuations (i.e., k types of agents). For exact EFX, it is known that an EFX allocation always exists when there are at most three types of agents. For approximate EFX, the best known guarantee is a 0.618-EFX allocation, and this has been improved recently to a φ-EFX allocation when the number of agents is at most seven. We settle another natural case in this landscape by showing that a φ-EFX allocation exists for any number of agents whenever there are at most four distinct valuations. We then consider a relaxation, EFX with charity, where some goods may remain unallocated and no agent envies the set of unallocated goods. It is known that, for n agents and any ε ∈ (0, 1/2], there exists an EFXε allocation with at most Õ((n/ε)^(1/2)) goods allocated to charity. We prove that when there are at most k distinct valuation types, there exists an EFXε allocation with only Õ((k/ε)^(1/2)) goods allocated to charity; in particular, the required amount of charity is sublinear in the number of distinct valuations rather than in the number of agents. We show that any EFX guarantee for k types of agents can be extended, with an additional (1 − 2ε) approximation factor, to a more general setting where the valuations can be partitioned into k clusters such that the maximum heterogeneity of valuations within each cluster is at most ε.
We introduce and study the multi-agent stochastic shortest path (MSSP) problem, in which k agents strive to reach a target state, aiming to minimize the expected time to reach the target by any agent. We analyze the computational and strategy-complexity of the problem in both autonomous and coordinated settings, and we design efficient strategy-synthesis algorithms. The algorithms are experimentally evaluated on instances of increasing size against natural baselines.
Many multiagent systems depend on collective decisions made by self-interested agents, which raises deep questions about coalition formation and stability. We study social choice with endogenous, outcome-contingent transfers, where agents voluntarily form contracts that redistribute utility depending on the collective decision, allowing for fully strategic coalition formation. We show that under consensus rules, individually rational strong Nash equilibria (IR–SNE) always exist, implementing welfare-maximizing outcomes with feasible transfers, and provide a simple, efficient algorithm to construct them. For more general anonymous, monotonic, and resolute rules, we identify necessary conditions for viable deviations, significantly limiting the possibility of destabilizing coalitions. By bridging cooperative and noncooperative perspectives, our approach shows that transferable utility can achieve core-like stability, restoring efficiency and budget balance even where classical impossibility results generally apply. Overall, this framework offers a practical and robust way to coordinate large-scale strategic multiagent systems.
Existing Autonomous Mobility-on-Demand (AMoD) systems and demand-responsive algorithms are designed to adaptively respond to traffic demands, enhancing traffic service quality and profitability. However, such approaches may exacerbate traffic congestion by concentrating vehicles in high-demand areas. In addition, repeated braking, acceleration, and low-speed driving in traffic jams lead to substantial increases in emissions. Moreover, existing Deep Reinforcement Learning (DRL)-based approaches fail to address the instability of cooperative learning in environments with highly variable rewards, such as carbon emissions. To address these issues, we propose the Spatio-Temporal Attention Rebalancing (STAR) framework, leveraging an encoder-decoder architecture. In the proposed framework, we maximize the number of requests served and minimize CO₂ emissions, while ensuring high service quality by limiting maximum travel delays and waiting times for passengers. To evaluate the proposed framework, we conduct simulations in realistic urban traffic scenarios. Experimental results demonstrate that our framework consistently outperforms existing baselines. In a large-scale scenario with a fleet of one hundred vehicles, our approach improves the service rate by up to 10.1% and reduces CO₂ emissions per passenger by up to 69.6% compared to the baseline methods. The proposed framework and baselines are publicly available at https://github.com/2jungeuni/eco-friendly-fleet-rebalancing.
Real-world multi-agent systems, from traffic coordination to resource allocation, are often modeled as general-sum games where individual incentives conflict with collective welfare. In these settings, the central challenge is not merely finding an equilibrium, but selecting socially desirable outcomes among many suboptimal Nash equilibria. Standard deep multi-agent reinforcement learning (MARL) methods struggle with this problem, as value-decomposition approaches are constrained by monotonicity assumptions and policy-gradient methods often converge to stable but socially inefficient equilibria. To address this limitation, we propose Phi-Actor-Critic (Phi-AC), a framework that leverages swap regret minimization to steer learning toward high-welfare correlated equilibria (CE). To make counterfactual regret estimation tractable in deep MARL, Phi-AC employs a centralized attention critic that predicts vector-valued regrets in a single forward pass, avoiding computationally expensive counterfactual simulations. We further introduce a Lagrangian-based equilibrium selection mechanism that optimizes social welfare while enforcing stability through regret constraints. Experiments on matrix games, Multi-Agent Particle Environments (MPE), and the Melting Pot Harvest scenario demonstrate that Phi-AC learns efficient and stable coordination strategies across diverse mixed-motive settings while maintaining high collective return and competitive fairness.
Agents implemented using Large Language Models (LLMs) offer novel solutions for tasks such as document summarization. However, single-agent systems, limited by their own knowledge base, often exhibit information omissions or inconsistencies with the facts, while multi-agent systems lacking effective organization can fall into the trap of social cognitive defects such as flattery and premature consensus. Inspired by the U.S. jury system, we propose JURIS, a judicial-decision-inspired multi-agent collaborative framework. Specifically, the document summarization process simulates a lawsuit scenario: multiple generator agents condense the target text into multiple sentences from different perspectives, much like lawyers on both sides providing different evidence; multiple decision-making agents consider the overall picture based on defense and voting mechanisms to select candidate sentences, much like a jury adopting different evidence; finally, a chief editor agent compiles a summary of all selected sentences, much like a secretary summarizing a plan and a judge giving a final verdict. Extensive experiments on in-domain news and cross-domain benchmarks demonstrate that JURIS consistently and significantly outperforms strong single-agent and multi-agent baselines across automatic evaluation metrics, multi-dimensional quality assessments, and human judgments, validating the effectiveness of decision-driven structured multi-agent collaboration for document summarization.
LLM-based role-playing has rapidly improved in fidelity, yet stronger adherence to persona constraints commonly increases vulnerability to jailbreak attacks, especially for risky or negative personas. Most prior work mitigates this issue with training-time solutions (e.g., data curation or alignment-oriented regularization). However, these approaches are costly to maintain as personas and attack strategies evolve, can degrade in-character behavior, and are typically infeasible for frontier closed-weight LLMs. We propose a training-free Dual-Cycle Adversarial Self-Evolution framework with two coupled cycles. A Persona-Targeted Attacker Cycle synthesizes progressively stronger jailbreak prompts, while a Role-Playing Defender Cycle distills observed failures into a hierarchical knowledge base of (i) global safety rules, (ii) persona-grounded constraints, and (iii) safe in-character exemplars. At inference time, the Defender retrieves and composes structured knowledge from this hierarchy to guide generation, producing responses that remain faithful to the target persona while satisfying safety constraints. Extensive experiments across multiple proprietary LLMs show consistent gains over strong baselines on both role fidelity and jailbreak resistance, and robust generalization to unseen personas and attack prompts.
In Partially Cooperative Markov Games (PCMG), agents need to learn effective cooperation under individual rewards, with the key challenge lies in leveraging these rewards to enhance team benefits optimally. Model aggregation (MA) is a promising solution due to its simplicity and efficiency, yet it suffers from instability caused by the volatility of individual policies trained with individual rewards and the non-asymptotic nature of aggregation updates. To address these challenges, we propose Two-Stage Model Aggregation (TSMA), a novel multi-policy MA framework for multi-agent reinforcement learning (MARL) that leverages individual policies to enhance team cooperation. Specifically, to enhance the stability and expressiveness of individual policies, each TSMA agent trains two individual policies (trained using the same individual reward) with parameter-level variation and combines them via adaptive weighted aggregation. The aggregated individual policy is then integrated with the team policy (trained using team reward), with integration weights dynamically adjusted over training. Additionally, L2 regularization is applied during the data-driven training to align their parameter distributions across policies, mitigating instability from non-asymptotic aggregation. As a general framework, TSMA is compatible with standard actor-critic MARL algorithms. We integrate TSMA with MAPPO and MADDPG, and evaluate them on challenging PettingZoo benchmarks, demonstrating significant improvements in PCMG. The code is available at: https://github.com/RL-DLMU/TSMA.
Bound-Independent Pruning (BIP) is a powerful technique for accelerating tree-based complete search algorithms for Distributed Constraint Optimization Problems (DCOPs) by pruning dominated regions of the search space using only local information. However, BIP fundamentally relies on constructing a context-dependent dominating space through joint optimization over local constraints, incurring exponential computational and storage complexity that limits its practical scalability. To address this limitation, we propose DR-BIP, a decoupled and sound reformulation of BIP that enables efficient identification of dominated subspaces without explicitly computing the dominating space. By reformulating dominated-subspace detection into pairwise dominance tests and decoupling them across independent constraints, DR-BIP eliminates joint optimization and reduces both computational and storage complexity from exponential to polynomial. The resulting dominance components can be precomputed and reused across context changes, further improving efficiency. We formally prove the correctness of DR-BIP and integrate it into several state-of-the-art tree-based complete DCOP algorithms. Extensive empirical evaluation on standard benchmarks confirms that DR-BIP consistently outperforms BIP, significantly reducing both computation time and communication overhead.