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Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 346/731 5. Nets and coalitions 2. Four Types of Nets Lemma 5.5 (O-Path reaches Global Optimum) A path of O-contracts always exists from any task allocation to the optimal one. The length of the shortest such path is at most |T |. Does that solve our problem? (Lookahead) Definition 5.6 (Task Allocation Graph) The task allocation graph has as vertices all possible task allocations (i.e. |A| |T | ) and directed edges from one vertex to another if there is a possible contract leading from one to the other. For O-contracts, searching the graph using breadth-first search takes how much time?
Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 347/731 5. Nets and coalitions 2. Four Types of Nets Lemma 5.7 (Allocation graph for O contracts is sparse) We assume that there are at least 2 agents and 2 tasks. We consider the task allocation graph for O contracts. Then the fraction number of edges number of edges in the fully connected graph converges to 0 both for |T | → ∞ as well as |A| → ∞
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1. Introduction 3. Formal Descripti
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2. Basic Architectures 2. BDI-Archi
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2. Basic Architectures 3. AOP Prof.
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3. Decision Making (1) 3. (Im-) Per
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6. Propositional Logic 3. Sudoku Si
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6. Propositional Logic 3. Sudoku Se
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9. Agents based on FOL 1. First Ord
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9. Agents based on FOL 4. (Con-)Gol
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Situation independent functions dec
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9. Agents based on FOL 7. Reference
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