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Samir Aknine

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34 papers
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34

JAAMAS Journal 2026 Journal Article

An Extended Multi-Agent Negotiation Protocol

  • Samir Aknine
  • Suzanne Pinson
  • Melvin F. Shakun

Abstract This article presents a task allocation protocol that is efficient in time and tolerates crash failures in multi-agent systems. The protocol is an extension of the negotiation protocol defined by Smith and Davis [25, 26] for task allocation. Our extension of the Contract Net Protocol (1) enables an agent to manage several negotiation processes in parallel; (2) optimizes the length of the negotiation processes among agents; (3) reduces the contractors' decommitment situations; (4) enables the detection of failures of an agent participating in a negotiation process and prevents a negotiation process with blocked agents.

AAAI Conference 2025 Conference Paper

A Multiagent Path Search Algorithm for Large-Scale Coalition Structure Generation

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder
  • Tuomas Sandholm

Coalition structure generation (CSG), i.e. the problem of optimally partitioning a set of agents into coalitions to maximize social welfare, is a fundamental computational problem in multiagent systems. This problem is important for many applications where small run times are necessary, including transportation and disaster response. In this paper, we develop SALDAE, a multiagent path finding algorithm for CSG that operates on a graph of coalition structures. Our algorithm utilizes a variety of heuristics and strategies to perform the search and guide it. It is an anytime algorithm that can handle large problems with hundreds and thousands of agents. We show empirically on nine standard value distributions, including disaster response and electric vehicle allocation benchmarks, that our algorithm enables a rapid finding of high-quality solutions and compares favorably with other state-of-the-art methods.

AAAI Conference 2025 Short Paper

Hide Exposures by Removing Mastermind’s External Sources on Social Network (Student Abstract)

  • Nilanjana Saha
  • Narayan Changder
  • Redha Taguelmimt
  • Samir Aknine
  • Animesh Dutta

On social media, it is easy to see how people are connected and find the leader, or mastermind of a network. The mastermind is responsible for the planning of the activities in the network. Hiding the mastermind is important to carry out these activities. This raises the question for the mastermind: How effectively can the mastermind hide his connections to avoid being found? We propose an efficient heuristic algorithm called HERMES (Hide Exposures by Removing Mastermind’s External Sources) to address this. Experiments on Facebook and Google networks show that HERMES hides the mastermind more effectively than the state-of-the-art, achieving time gains of 103 and 1397 seconds, respectively, and improving influence value by up to 11.11%.

AAMAS Conference 2024 Conference Paper

A Multiagent Path Search Algorithm for Large-Scale Coalition Structure Generation

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder
  • Tuomas Sandholm

Coalition structure generation (CSG) is a critical problem in multiagent systems, involving the optimal partitioning of agents into disjoint coalitions to maximize social welfare. This paper introduces SALDAE, a novel multiagent path finding algorithm for CSG on a coalition structure graph. SALDAE employs various heuristics and strategies for efficient search, making it an anytime algorithm suitable for handling large-scale problems.

AAAI Conference 2024 Short Paper

Coalition Formation for Task Allocation Using Multiple Distance Metrics (Student Abstract)

  • Tuhin Kumar Biswas
  • Avisek Gupta
  • Narayan Changder
  • Redha Taguelmimt
  • Samir Aknine
  • Samiran Chattopadhyay
  • Animesh Dutta

Simultaneous Coalition Structure Generation and Assignment (SCSGA) is an important research problem in multi-agent systems. Given n agents and m tasks, the aim of SCSGA is to form m disjoint coalitions of n agents such that between the coalitions and tasks there is a one-to-one mapping, which ensures each coalition is capable of accomplishing the assigned task. SCSGA with Multi-dimensional Features (SCSGA-MF) extends the problem by introducing a d-dimensional vector for each agent and task. We propose a heuristic algorithm called Multiple Distance Metric (MDM) approach to solve SCSGA-MF. Experimental results confirm that MDM produces near optimal solutions, while being feasible for large-scale inputs within a reasonable time frame.

AAMAS Conference 2024 Conference Paper

Efficient Size-based Hybrid Algorithm for Optimal Coalition Structure Generation

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder
  • Tuomas Sandholm

Coalition Structure Generation (CSG) involves dividing agents into coalitions in such a way as to coordinate them into solving problems together efficiently. In this paper, we revisit the CSG problem and propose a new search method that introduces an offline phase to speed up the search process, where the best coalition sets to search are preprocessed. These sets are calculated only once regardless of the coalition values and can be reused each time a CSG instance is to be solved. Then our search in the online phase combines dynamic programming with integer partition-based search in a novel way.

IJCAI Conference 2024 Conference Paper

Faster Optimal Coalition Structure Generation via Offline Coalition Selection and Graph-Based Search

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder
  • Tuomas Sandholm

Coalition formation is a key capability in multi-agent systems. An important problem in coalition formation is coalition structure generation: partitioning agents into coalitions to optimize the social welfare. This is a challenging problem that has been the subject of active research for the past three decades. In this paper, we present a novel algorithm, SMART, for the problem based on a hybridization of three innovative techniques. Two of these techniques are based on dynamic programming, where we show a powerful connection between the coalitions selected for evaluation and the performance of the algorithms. These algorithms use offline phases to optimize the choice of coalitions to evaluate. The third one uses branch-and-bound and integer partition graph search to explore the solution space. Our techniques bring a new way of approaching the problem and a new level of precision to the field. In experiments over several common value distributions, we show that the hybridization of these techniques in SMART is faster than the fastest prior algorithms (ODP-IP, BOSS) in generating optimal solutions across all the value distributions.

ECAI Conference 2023 Conference Paper

Anytime Index-Based Search Method for Large-Scale Simultaneous Coalition Structure Generation and Assignment

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder

Organizing agents into disjoint groups is a crucial challenge in artificial intelligence, with many applications where quick runtime is essential. The Simultaneous Coalition Structure Generation and Assignment (SCSGA) problem involves partitioning a set of agents into coalitions and assigning each coalition to a task, with the goal of maximizing social welfare. However, this is an NP-complete problem, and only a few algorithms have been proposed to address it for both small and large-scale problems. In this paper, we address this challenge by presenting a novel algorithm that can efficiently solve both small and large instances of this problem. Our method is based on a new search space representation, where each coalition is codified by an index. We have developed an algorithm that can explore this solution space effectively by generating index vectors that represent coalition structures. The resulting algorithm is anytime and can scale to large problems with hundreds or thousands of agents. We evaluated our algorithm on a range of value distributions and compared its performance against state-of-the-art algorithms. Our experimental results demonstrate that our algorithm outperforms existing methods in solving the SCSGA problem, providing high-quality solutions for a wide range of problem instances.

IJCAI Conference 2023 Conference Paper

Optimal Anytime Coalition Structure Generation Utilizing Compact Solution Space Representation

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder
  • Tuomas Sandholm

Coalition formation is a central approach for multiagent coordination. A crucial part of coalition formation that is extensively studied in AI is coalition structure generation: partitioning agents into coalitions to maximize overall value. In this paper, we propose a novel method for coalition structure generation by introducing a compact and efficient representation of coalition structures. Our representation partitions the solution space into smaller, more manageable subspaces that gather structures containing coalitions of specific sizes. Our proposed method combines two new algorithms, one which leverages our compact representation and a branch-and-bound technique to generate optimal coalition structures, and another that utilizes a preprocessing phase to identify the most promising sets of coalitions to evaluate. Additionally, we show how parts of the solution space can be gathered into groups to avoid their redundant evaluation and we investigate the computational gain that is achieved by avoiding that redundant processing. Through this approach, our algorithm is able to prune the solution space more efficiently. Our results show that the proposed algorithm is superior to prior state-of-the-art methods in generating optimal coalition structures under several value distributions.

AAAI Conference 2023 Short Paper

Parallel Index-Based Search Algorithm for Coalition Structure Generation (Student Abstract)

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder

In this paper, we propose a novel algorithm to address the Coalition Structure Generation (CSG) problem. Specifically, we use a novel representation of the search space that enables it to be explored in a new way. We introduce an index-based exact algorithm. Our algorithm is anytime, produces optimal solutions, and can be run on large-scale problems with hundreds of agents. Our experimental evaluation on a benchmark with several value distributions shows that our representation of the search space that we combined with the proposed algorithm provides high-quality results for the CSG problem and outperforms existing state-of-the-art algorithms.

AAAI Conference 2021 Short Paper

BOSS: A Bi-directional Search Technique for Optimal Coalition Structure Generation with Minimal Overlapping (Student Abstract)

  • Narayan Changder
  • Samir Aknine
  • Sarvapali D. Ramchurn
  • Animesh Dutta

In this paper, we focus on the Coalition Structure Generation (CSG) problem, which involves finding exhaustive and disjoint partitions of agents such that the efficiency of the entire system is optimized. We propose an efficient hybrid algorithm for optimal coalition structure generation called BOSS. When compared to the state-of-the-art, BOSS is shown to perform better by up to 33.63% on benchmark inputs. The maximum time gain by BOSS is 3392 seconds for 27 agents.

AAAI Conference 2021 Short Paper

FACS: Fast Code-based Algorithm for Coalition Structure Generation (Student Abstract)

  • Redha Taguelmimt
  • Samir Aknine
  • Djamila Boukredera
  • Narayan Changder

In this paper, we propose a new algorithm for the Coalition Structure Generation (CSG) problem that can be run with more than 28 agents while using a complete set of coalitions as input. The current state-of-the-art limit for exact algorithms to solve the CSG problem within a reasonable time is 27 agents. Our algorithm uses a novel representation of the search space and a new code-based search technique. We propose an effective heuristic search method to efficiently explore the space of coalition structures using our code based technique and show that our method outperforms existing state-of-the-art algorithms by multiple orders of magnitude.

AAAI Conference 2021 Short Paper

Leveraging on Deep Reinforcement Learning for Autonomous Safe Decision-Making in Highway On-ramp Merging (Student Abstract)

  • Zine el abidine Kherroubi
  • Samir Aknine
  • Rebiha Bacha

High-speed highway on-ramp merging is one of the most difficult and critical tasks for any autonomous driving system. This work studies this problem by combining deep deterministic policy gradient (DDPG) reinforcement learning with drivers’ intentions prediction. Our proposed solution is based on an artificial neural network to predict drivers’ intentions, used as an input state to the DDPG agent that outputs the longitudinal acceleration to the merging vehicle. We show that this solution improves safety performances.

EAAI Journal 2020 Journal Article

Coalition formation with dynamically changing externalities

  • Youcef Sklab
  • Samir Aknine
  • Onn Shehory
  • AbdelKamel Tari

We consider multiple self-interested bounded-rational agents each of which has a goal it needs to achieve. Goals are achievable by executing a set of interdependent tasks. Some tasks exhibit time dependencies and may require sequential execution. For each agent, there may be several alternative sets of tasks that can achieve the goal. Execution of alternatives, may be more beneficial when done by a group of agents and not by a single agent. To jointly achieve goals, agents may form interdependent coalitions. Such coalition formation is computationally intractable. We nevertheless seek a practical solution that is not necessarily optimal yet acceptable by the agents. A solution where agents examine only coalitions in which they are members is inapplicable, as externalities are a major factor given task interdependencies. In this paper we study this coalition formation problem. We describe the problem and introduce a novel Multi-lateral Negotiation Protocol ( MNP ) that solves it by forming interdependent coalitions. We allow agents to heuristically make gradual concessions, revise their proposals and converge on specific alternatives, and nevertheless increase their expected gains.

EUMAS Conference 2020 Conference Paper

Decentralised Control of Intelligent Devices: A Healthcare Facility Study

  • Sacha Lhopital
  • Samir Aknine
  • Vincent Thavonekham
  • Huan Vu
  • Sarvapali D. Ramchurn

Abstract We present a novel approach to the management of notifications from devices in a healthcare setting. We employ a distributed constraint optimisation (DCOP) approach to the delivery of notification for healthcare assistants that aims to preserve the privacy of patients while reducing the intrusiveness of such notifications. Our approach reduces the workload of the assistants and improves patient safety by automating task allocation while ensuring high priority needs are addressed in a timely manner. We propose and evaluate several DCOP models both in simulation and in real-world deployments. Our models are shown to be efficient both in terms of computation and communication costs.

EUMAS Conference 2020 Conference Paper

Decentralised Multi-intersection Congestion Control for Connected Autonomous Vehicles

  • Huan Vu
  • Samir Aknine
  • Sarvapali D. Ramchurn
  • Alessandro Farinelli

Abstract This paper presents a decentralised mechanism for traffic control of connected autonomous vehicles in settings where multiple road intersections have to be managed and optimised. We propose a solution based on the distributed constraint optimisation approach (DCOP). We build upon state of the art algorithm for single-intersection management in order to manage congestion both across and within intersections. Furthermore, to solve the DCOP, we propose an improved node ordering policy for the Max-sum_AD_VP algorithm. Empirical evaluation of our model and algorithm demonstrate that our approach outperforms existing benchmarks by up to 32% in terms of average delay for both single and multiple intersection setup.

EUMAS Conference 2020 Conference Paper

Distributed Multi-issue Multi-lateral Negotiation Using a Divide and Rule Approach

  • Ndeye Arame Diago
  • Samir Aknine
  • Sarvapali D. Ramchurn
  • El hadji Ibrahima Diago

Abstract In this paper, we consider the problem of multi-issue multi-lateral negotiation. We assume that each agent may be interested only in a subset of issues at stake. They nevertheless have to make a collective choice that addresses all issues. We propose a heuristics-based negotiation model where the agents’reasoning mechanisms may be very complex as a result of multiple issues being negotiated. Given this complexity, we propose a distributed negotiation mechanism drawn on divide and rule. The proposed protocol consists of two iterative steps: the partitioning of the agents into groups and the negotiation step where the agents in each group interact without a central controller (no mediator). Our negotiation protocol converges and leads to efficient outcomes, as demonstrated by our empirical results.

AAAI Conference 2020 Conference Paper

ODSS: Efficient Hybridization for Optimal Coalition Structure Generation

  • Narayan Changder
  • Samir Aknine
  • Sarvapali Ramchurn
  • Animesh Dutta

Coalition Structure Generation (CSG) is an NP-complete problem that remains difficult to solve on account of its complexity. In this paper, we propose an efficient hybrid algorithm for optimal coalition structure generation called ODSS. ODSS is a hybrid version of two previously established algorithms IDP (Rahwan and Jennings 2008) and IP (Rahwan et al. 2009). ODSS minimizes the overlapping between IDP and IP by dividing the whole search space of CSG into two disjoint sets of subspaces and proposes a novel subspace shrinking technique to reduce the size of the subspace searched by IP with the help of IDP. When compared to the state-of-the-art against a wide variety of value distributions, ODSS is shown to perform better by up to 54. 15% on benchmark inputs.

AAAI Conference 2019 Short Paper

An Imperfect Algorithm for Coalition Structure Generation

  • Narayan Changder
  • Samir Aknine
  • Animesh Dutta

Optimal Coalition Structure Generation (CSG) is a significant research problem that remains difficult to solve. Given n agents, the ODP-IP algorithm (Michalak et al. 2016) achieves the current lowest worst-case time complexity of O(3n). We devise an Imperfect Dynamic Programming (ImDP) algorithm for CSG with runtime O(n2n). Imperfect algorithm means that there are some contrived inputs for which the algorithm fails to give the optimal result. Experimental results confirmed that ImDP algorithm performance is better for several data distribution, and for some it improves dramatically ODP-IP. For example, given 27 agents, with ImDP for agentbased uniform distribution time gain is 91% (i.e. 49 minutes).

SoCS Conference 2019 Conference Paper

An Improved Algorithm for Optimal Coalition Structure Generation

  • Narayan Changder
  • Samir Aknine
  • Animesh Dutta

The Coalition Structure Generation (CSG) problem is a partitioning of a set of agents into exhaustive and disjoint coalitions to maximize social welfare. This NP-complete problem arises in many practical scenarios. Prominent examples are included in the field of transportation, e-Commerce, distributed sensor networks, and others. The fastest exact algorithm to solve the CSG problem is ODP-IP, which is a hybrid version of two previously established algorithms, namely Improved Dynamic Programming (IDP) and IP. In this paper, we show that the ODP-IP algorithm performs many redundant operations. To improve ODP-IP, we propose a faster abortion mechanism to speed up IP’s search. Our abortion mechanism decides at runtime which of the IP

AAMAS Conference 2019 Conference Paper

Dynamic and Intelligent Control of Autonomous Vehicles for Highway On-ramp Merge

  • Zine el abidine Kherroubi
  • Samir Aknine
  • Rebiha Bacha

This work addresses the problem of predicting the intentions of drivers in a highway on-ramp situation using a dynamic Bayesian network. We present the proposed model and detail its use. Then, we report the simulation results that show good performances for predicting highway on-ramp merging intentions.

IJCAI Conference 2018 Conference Paper

A Decentralised Approach to Intersection Traffic Management

  • Huan Vu
  • Samir Aknine
  • Sarvapali D. Ramchurn

Traffic congestion has a significant impact on quality of life and the economy. This paper presents a decentralised traffic management mechanism for intersections using a distributed constraint optimisation approach (DCOP). Our solution outperforms the state of the art solution both for stable traffic conditions (about 60% reduced waiting time) and robustness to unpredictable events.

ECAI Conference 2016 Conference Paper

Managing Energy Markets in Future Smart Grids Using Bilateral Contracts

  • Romain Caillière
  • Samir Aknine
  • Antoine Nongaillard
  • Sarvapali D. Ramchurn

Future smart grids will empower home owners to buy energy from real-time markets, coalesce into energy cooperatives, and sell energy they generate from their local renewable energy sources. Such interactions by large numbers of small prosumers (that both consume and produce) will engender potentially unpredictable fluctuations in energy prices which could be detrimental to all actors in the system. Hence, in this paper, we propose negotiation mechanisms to orchestrate such interactions as well as pricing mechanisms to help stabilise energy prices on multiple time scales. We then prove 1) that our solution guarantees that, while prices fluctuations can be constrained, 2) that it is individually rational for agents to join energy cooperatives and 3) that the negotiation mechanisms we employ result in pareto-optimal solutions.

AAMAS Conference 2016 Conference Paper

Multi-Agent Mechanism for Efficient Cooperative Use of Energy (Extended Abstract)

  • Romain François Cailliere
  • Samir Aknine
  • Antoine Nongaillard

Promoting the development of renewable energies and the efficient and intelligent use of energy could be achieved through making adaptive consumer demands to energy supply. In this paper, we propose a mechanism based on three time scales, year, day and hour and three sets of agents, consumers, aggregators and providers to adapt consumption to production. We propose to use in this model the breakthroughs in energy: grouping consumers to reduce deviation in aggregated demand, Time-of-Use and Prediction-of-Use tariff schemes, storage capacities, shifting and the possibility for consumers to produce energy. CCS Concepts •Computing methodologies → Multi-agent systems; Multi-agent planning;

EUMAS Conference 2014 Conference Paper

Modeling a Multi-issue Negotiation Protocol for Agent Extensible Negotiations

  • Samir Aknine
  • Souhila Arib
  • Djamila Boukredera

Abstract In this paper, we study how to achieve more effective negotiations by extending during the negotiation process, the negotiation object with new relevant items. Indeed, the possibility to extend the initial set of items defined by the requester agent with other items related to the original query can help find an agreement. In doing so, with extended proposals, the requester agent may be incentivized to be more flexible, e. g. , by making concessions or relaxing some constraints on the issues. This may help to achieve an agreement which is more beneficial for both parties than breaking down the negotiation. Such extensible negotiations may lead to win-win outcomes which otherwise can not be achieved with some usual negotiation strategies where it is hard to dynamically alter the set of items under negotiation during the course of the process. In this paper, we first outline a negotiation strategy which allows the extension of the negotiation space by extending the negotiation object with new relevant items. Based on this, we then propose a new multi-issue negotiation protocol which relies on the bidding-based mechanism and deals with such extensible negotiation strategies.

ECAI Conference 2010 Conference Paper

Coalition Formation Strategies for Self-Interested Agents in Hedonic Games

  • Thomas Génin
  • Samir Aknine

In this article, we address the problem of coalition formation in multiagent systems. Our work focuses on the class of hedonic games, where the satisfaction of each agent depends on other agents taking part in the coalition. We present in this paper some strategies, which could be used by agents. We describe two types of strategies: proposal acceptance strategies, which allow agents to accept or reject a coalition formation proposal and proposal selection strategies based on the analysis of the history of a negotiation, which allow agents to select interesting coalitions to propose. We underline that a compromise between high and low selectivity allows agents to obtain a higher probability to form coalitions with a satisfying utility. Our proposal selection strategies allow agents to reduce the number of proposals to send during the coalition formation process without losing much utility. This speeds up considerably the process.

ECAI Conference 2008 Conference Paper

Coalition Formation Strategies for Self-Interested Agents

  • Thomas Génin
  • Samir Aknine

Coalition formation is a major research issue in multiagent systems in which the agents are self-interested. In these systems, agents have to form groups in order to achieve common goals, which they are not able to achieve individually. A coalition formation mechanism requires two definition levels: firstly agents need a common protocol to reach an agreement and secondly individual strategies are required to make efficient proposals. Both issues are addressed in this paper. First, we propose a two-phase decentralized protocol that allows agents to interact directly through message passing. Secondly we propose some strategies which allow agents to make clever proposals using the information that has already been collected from other agents. The experimental evaluation shows that the proposed mechanism allows agents to efficiently form coalitions and that the strategies make real improvements for the coalition search process.

AAMAS Conference 2007 Conference Paper

Predictive Fault Tolerance in Multi-Agent Systems: a Plan-Based Replication Approach

  • Alessandro de Luna Almeida
  • Samir Aknine
  • Jean-Pierre Briot
  • Jacques Malenfant

The fact that multi-agent applications are prone to the same faults that any distributed system is susceptible to and the need for a higher quality of service in these systems justify the increasing interest in fault-tolerant multi-agent systems. In this article, we propose an original method for providing dependability in multiagent systems through replication. Our method is different from other works because our research focuses on building an automatic, adaptive and predictive replication policy where critical agents are replicated to minimize the impact of failures. This policy is determined by taking into account the criticality of the plans of the agents, which contain the collective and individual behaviors of the agents in the application. The set of replication strategies applied at a given moment to an agent is then fine-tuned gradually by the replication system so as to reflect the dynamicity of the multi-agent system. Some preliminary measurements were made to assess the efficiency of our approach and future directions are presented.

ECAI Conference 2006 Conference Paper

Reaching Agreements for Coalition Formation Through Derivation of Agents' Intentions

  • Samir Aknine
  • Onn Shehory

This paper addresses the coalition formation problem in multiagent systems. Although several coalition formation models exist today, coalition formation using these models remains costly. As a consequence, applying these models through several iterations when required becomes time-consuming. This paper proposes a new coalition formation mechanism (CFM) to reduce this execution cost. This mechanism is based on four principles: (1) the use of information on task relationships so as to reduce the computational complexity of the coalition formation; (2) the exploitation of the coalition proposals formulated by certain agents in order to derive their intentions, (this principle makes the search for solutions easier, which in turn may result in earlier consensus and agreements-the intention derivation process is performed on a new graph structure introduced in this paper); (3) the use of several strategies for propagating the proposals of the agents in the coalition formation process; and (4) the dynamic reorganization of previous coalitions.

ECAI Conference 2006 Conference Paper

Search Better and Gain More: Investigating New Graph Structures for Multi-Agent Negotiations

  • Samir Aknine

Combined negotiation in multi-agent systems is a hard task since it involves several levels of difficulty. In order to improve their payoff, first agents behave in a strategic manner while bargaining since they need to deal with various types of behaviors. Second agents have to react to the proposals of other agents in finding the optimal solutions for their negotiation. This paper tackles the problem of winner determination in combined multi-agent negotiations and addresses two fundamental issues. The first contribution of this work is a winner determination algorithm, which finds an optimal solution, which is a combination of several bids selected from a set of bids at one iteration of a combined negotiation. In addition, the problem of dynamically revising these optimal solutions with regards to changes on bids is considered. These changes occur in multi-agent negotiation processes having several iterations and which use multi-phased protocols. To date no work addresses this problem. The second contribution of this work is an iterative algorithm for updating the optimal solutions to avoid integral and repetitive reapplication of the winner determination algorithm. The results of the experiments carried out using our algorithms have confirmed the importance and the originality of our approach based on the use of shared and unshared item graphs.

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