A polynomial-time algorithm for the maximum cardinality cut problem in proper interval graphs

2017 ◽  
Vol 121 ◽  
pp. 29-33
Author(s):  
Arman Boyacı ◽  
Tinaz Ekim ◽  
Mordechai Shalom
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Interval Graphs ◽  
Maximum Cardinality

scholarly journals Computing the Weighted Isolated Scattering Number of Interval Graphs in Polynomial Time

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Fengwei Li ◽  
Xiaoyan Zhang ◽  
Qingfang Ye ◽  
Yuefang Sun
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Interval Graphs ◽  
Perfect Graphs ◽  
Network Vulnerability ◽  
Hamiltonian Properties

The scattering number and isolated scattering number of a graph have been introduced in relation to Hamiltonian properties and network vulnerability, and the isolated scattering number plays an important role in characterizing graphs with a fractional 1-factor. Here we investigate the computational complexity of one variant, namely, the weighted isolated scattering number. We give a polynomial time algorithm to compute this parameter of interval graphs, an important subclass of perfect graphs.

scholarly journals Maximum Cardinality 1-Restricted Simple 2-Matchings

10.37236/991 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
David Hartvigsen
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Hamilton Cycle ◽  
Connected Component ◽  
Maximum Cardinality

A simple 2-matching in a graph is a subgraph all of whose nodes have degree $1$ or $2$. A simple 2-matching is called $k$-restricted if every connected component has $>k$ edges. We consider the problem of finding a $k$-restricted simple 2-matching with a maximum number of edges, which is a relaxation of the problem of finding a Hamilton cycle in a graph. Our main result is a min-max theorem for the maximum number of edges in a 1-restricted simple 2-matching. We prove this result constructively by presenting a polynomial time algorithm for finding a 1-restricted simple 2-matching with a maximum number of edges.

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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