A polynomial time algorithm for the computation of the iteration-period bound in recursive data flow graphs

1992 ◽  
Vol 39 (1) ◽  
pp. 49-52 ◽  
Author(s):  
S.H. Gerez ◽  
S.M. Heemstra de Groot ◽  
O.E. Herrmann
Keyword(s):  
Polynomial Time ◽  
Data Flow ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Iteration Period ◽  
Data Flow Graphs ◽  
Recursive Data ◽  
Flow Graphs

The cost of a cycle is a square

2002 ◽  
Vol 67 (1) ◽  
pp. 35-60 ◽  
Author(s):  
A. Carbone
Keyword(s):  
Lower Bounds ◽  
Polynomial Time ◽  
Heuristic Algorithms ◽  
Sequent Calculus ◽  
Propositional Calculus ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Proof Search ◽  
The Cost ◽  
Flow Graphs

AbstractThe logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be non-elementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an acyclic proof with (kn+1) lines. In particular, there is a polynomial time algorithm which eliminates cycles from a proof. These results are motivated by the search for general methods on proving lower bounds on proof size and by the design of more efficient heuristic algorithms for proof search.

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.

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