scholarly journals Recognizing k-leaf powers in polynomial time, for constant k

2022 ◽  
pp. 1384-1410
Author(s):  
Manuel Lafond
Keyword(s):  
Polynomial Time

The 2-closure of a 32-transitive group in polynomial time

2018 ◽  
Vol 60 (2) ◽  
pp. 360-375
Author(s):  
A. V. Vasil'ev ◽  
D. V. Churikov
Keyword(s):  
Polynomial Time ◽  
Transitive Group

Learning Importance of Preferences

10.29007/v68w ◽  
2018 ◽  
Author(s):  
Ying Zhu ◽  
Mirek Truszczynski
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Scoring Rules ◽  
Np Hard ◽  
Individual Preferences

We study the problem of learning the importance of preferences in preference profiles in two important cases: when individual preferences are aggregated by the ranked Pareto rule, and when they are aggregated by positional scoring rules. For the ranked Pareto rule, we provide a polynomial-time algorithm that finds a ranking of preferences such that the ranked profile correctly decides all the examples, whenever such a ranking exists. We also show that the problem to learn a ranking maximizing the number of correctly decided examples (also under the ranked Pareto rule) is NP-hard. We obtain similar results for the case of weighted profiles when positional scoring rules are used for aggregation.

scholarly journals Learn your opponent's strategy (in polynomial time)!

1996 ◽  
pp. 164-176 ◽  
Author(s):  
Yishay Mor ◽  
Claudia V. Goldman ◽  
Jeffrey S. Rosenschein
Keyword(s):  
Polynomial Time

On the Complexity of Deadlock Recovery

1986 ◽  
Vol 9 (3) ◽  
pp. 323-342
Author(s):  
Joseph Y.-T. Leung ◽  
Burkhard Monien
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Arbitrary Number ◽  
The Other ◽  
Np Hard ◽  
Total Cost ◽  
Other Hand ◽  
Input Parameters ◽  
Resource Type

We consider the computational complexity of finding an optimal deadlock recovery. It is known that for an arbitrary number of resource types the problem is NP-hard even when the total cost of deadlocked jobs and the total number of resource units are “small” relative to the number of deadlocked jobs. It is also known that for one resource type the problem is NP-hard when the total cost of deadlocked jobs and the total number of resource units are “large” relative to the number of deadlocked jobs. In this paper we show that for one resource type the problem is solvable in polynomial time when the total cost of deadlocked jobs or the total number of resource units is “small” relative to the number of deadlocked jobs. For fixed m ⩾ 2 resource types, we show that the problem is solvable in polynomial time when the total number of resource units is “small” relative to the number of deadlocked jobs. On the other hand, when the total number of resource units is “large”, the problem becomes NP-hard even when the total cost of deadlocked jobs is “small” relative to the number of deadlocked jobs. The results in the paper, together with previous known ones, give a complete delineation of the complexity of this problem under various assumptions of the input parameters.

scholarly journals The Fair Division of Hereditary Set Systems

2021 ◽  
Vol 9 (2) ◽  
pp. 1-19
Author(s):  
Z. Li ◽  
A. Vetta
Keyword(s):  
Recent Work ◽  
Polynomial Time ◽  
Simple Algorithm ◽  
Fair Division ◽  
Set Systems

We consider the fair division of indivisible items using the maximin shares measure. Recent work on the topic has focused on extending results beyond the class of additive valuation functions. In this spirit, we study the case where the items form a hereditary set system. We present a simple algorithm that allocates each agent a bundle of items whose value is at least 0.3666 times the maximin share of the agent. This improves upon the current best known guarantee of 0.2 due to Ghodsi et al. The analysis of the algorithm is almost tight; we present an instance where the algorithm provides a guarantee of at most 0.3738. We also show that the algorithm can be implemented in polynomial time given a valuation oracle for each agent.

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