scholarly journals Convexity of b-matching Games

2020 ◽  
Author(s):  
Soh Kumabe ◽  
Takanori Maehara
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kidney Exchange ◽  
The Core ◽  
Emptiness Problem ◽  
Matching Games ◽  
Matching Game ◽  
Necessary And Sufficient

The b-matching game is a cooperative game defined on a graph. The game generalizes the matching game to allow each individual to have more than one partner. The game has several applications, such as the roommate assignment, the multi-item version of the seller-buyer assignment, and the international kidney exchange. Compared with the standard matching game, the b-matching game is computationally hard. In particular, the core non-emptiness problem and the core membership problem are co-NP-hard. Therefore, we focus on the convexity of the game, which is a sufficient condition of the core non-emptiness and often more tractable concept than the core non-emptiness. It also has several additional benefits. In this study, we give a necessary and sufficient condition of the convexity of the b-matching game. This condition also gives an O(n log n + m α(n)) time algorithm to determine whether a given game is convex or not, where n and m are the number of vertices and edges of a given graph, respectively, and α(・) is the inverse-Ackermann function. Using our characterization, we also give a polynomial-time algorithm to compute the Shapley value of a convex b-matching game.

SYSTOLIC TREE WITH BASE AUTOMATA

1991 ◽  
Vol 02 (03) ◽  
pp. 221-236 ◽  
Author(s):  
A. MONTI ◽  
D. PARENTE
Keyword(s):  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Emptiness Problem ◽  
Necessary And Sufficient ◽  
Natural Way

Different systolic tree automata (STA) with base (T(b)−STA) are compared. This is a subclass of STA with interesting properties of modularity. We give a necessary and sufficient condition for the inclusion between classes of languages accepted by T(b)− STA, (L(T(b)−STA)), as b varies. We focus on T(b)−STA obtained by varying the base b in a natural way. We prove that for every base b within this framework there exists an a such that L(T(a)−STA) is not contained in L(T(b)−STA). We characterize the family of languages accepted by T(b)−STA when the input conditions are relaxed. Moreover we show that the emptiness problem is decidable for T(b)−STA.

Individual Testing of Independent Items in Optimal Group Testing

1988 ◽  
Vol 2 (1) ◽  
pp. 23-29 ◽  
Author(s):  
Y. C. Yao ◽  
F. K. Hwang
Keyword(s):  
Group Testing ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Necessary And Sufficient Condition ◽  
Expected Number ◽  
Testing Problem ◽  
The Individual ◽  
Testing Algorithm ◽  
Necessary And Sufficient ◽  
Special Case

We consider the group testing problem for a set of independent items I = [I1,… In] where Ii, has probability pi, of being defective and probability qi = 1 – pi of being good. The problem is to classify all items as good or defective with a minimum expected number of group tests where a group test is a test on a subset S of I with two possible outcomes: either S is pure (contains no defective) or S is contaminated (contains at least one defective, with no information provided about which or how many). No polynomial-time algorithm is known for the group testing problem even for the special case pi = p for all i. Hence, any method that reduces the size of the problem is very helpful. In this paper, we give such a method by providing a simple condition to screen items that should be tested (only) individually. This condition leads to a necessary and sufficient condition for the individual testing algorithm to be optimal, generalizing a result of Unger [1] for the special case of identical pi.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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