Download PDF by Toby Walsh: Algorithmic Decision Theory: 4th International Conference,

By Toby Walsh

ISBN-10: 3319231138

ISBN-13: 9783319231136

ISBN-10: 3319231146

ISBN-13: 9783319231143

This booklet constitutes the completely refereed convention complaints of the 4th overseas convention on Algorithmic determination concept , ADT 2015, held in September 2015 in Lexington, united states. The 32 complete papers provided have been conscientiously chosen from seventy six submissions. The papers are prepared in topical sections comparable to personal tastes; manipulation, studying and different matters; software and determination idea; argumentation; bribery and keep an eye on; social selection; allocation and different difficulties; doctoral consortium.

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Extra resources for Algorithmic Decision Theory: 4th International Conference, ADT 2015, Lexington, KY, USA, September 27-30, 2015, Proceedings

Example text

2. Let A := A∗ \ A2 . Let G = (V, E) with V = N ∪ A , E = {{i, a}|i ∈ N, a ∈ A , (a, 1) ∈ Si }. Compute a maximum cardinality matching M in G. For a ∈ A , assign agent i to a if {i, a} ∈ M . It is not hard to verify that the resulting assignment π is in fact an individually rational assignment of maximum score. Group Activity Selection from Ordinal Preferences 43 Theorem 5. For any k ≤ 3, in o-GASP with k-approval scores, in the case of decreasing preferences an individually rational assignment of maximum score can be found in polynomial time.

Consequently, preference representation languages and algorithms for reasoning about preferences have received substantial attention [8]. When there are only a few objects (or outcomes) to compare, it is both most direct and feasible to represent preference orders by their explicit enumerations. The situation changes when the domain of interest is combinatorial, that is, its elements are described in terms of combinations of values of issues, say x1 , . . , xn (also called variables or attributes), with each issue xi assuming values from some set Di — its domain.

Definition 2. Optimality-testing (OptTest): given a P-tree T and an outcome M of T , decide whether M is optimal. Definition 3. Optimality-with-property (OptProp): given a P-tree T and some property α expressed as a Boolean formula over the vocabulary of T , decide whether there is an optimal outcome M that satisfies α. Our first result shows that P-trees support efficient dominance testing. Theorem 4. The DomTest problem can be solved in time linear in the height of the P-tree T . Proof. The DomTest problem can be solved by walking down the tree.

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Algorithmic Decision Theory: 4th International Conference, ADT 2015, Lexington, KY, USA, September 27-30, 2015, Proceedings by Toby Walsh


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