scholarly journals On Finding and Enumerating Maximal and Maximum k-Partite Cliques in k-Partite Graphs

Algorithms ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 23 ◽  
Author(s):  
Charles Phillips ◽  
Kai Wang ◽  
Erich Baker ◽  
Jason Bubier ◽  
Elissa Chesler ◽  
...  
Keyword(s):  
Functional Genomics ◽  
Polynomial Time ◽  
Special Class ◽  
Bipartite Graphs ◽  
Time Transformation ◽  
Np Hard ◽  
Maximum Element ◽  
Heuristic Approaches ◽  
Upper Limit ◽  
Open Questions

Let k denote an integer greater than 2, let G denote a k-partite graph, and let S denote the set of all maximal k-partite cliques in G. Several open questions concerning the computation of S are resolved. A straightforward and highly-scalable modification to the classic recursive backtracking approach of Bron and Kerbosch is first described and shown to run in O(3n/3) time. A series of novel graph constructions is then used to prove that this bound is best possible in the sense that it matches an asymptotically tight upper limit on |S|. The task of identifying a vertex-maximum element of S is also considered and, in contrast with the k = 2 case, shown to be NP-hard for every k ≥ 3. A special class of k-partite graphs that arises in the context of functional genomics and other problem domains is studied as well and shown to be more readily solvable via a polynomial-time transformation to bipartite graphs. Applications, limitations, potentials for faster methods, heuristic approaches, and alternate formulations are also addressed.

scholarly journals Polynomial time recognition of vertices contained in all (or no) maximum dissociation sets of a tree

2021 ◽  
Vol 7 (1) ◽  
pp. 569-578
Author(s):  
Jianhua Tu ◽  
◽  
Lei Zhang ◽  
Junfeng Du ◽  
Rongling Lang ◽  
...  
Keyword(s):  
Polynomial Time ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Recognition Algorithm ◽  
Vertex Degree ◽  
Np Hard ◽  
Maximum Cardinality

<abstract><p>In a graph $ G $, a dissociation set is a subset of vertices which induces a subgraph with vertex degree at most 1. Finding a dissociation set of maximum cardinality in a graph is NP-hard even for bipartite graphs and is called the maximum dissociation set problem. The complexity of the maximum dissociation set problem in various sub-classes of graphs has been extensively studied in the literature. In this paper, we study the maximum dissociation problem from different perspectives and characterize the vertices belonging to all maximum dissociation sets, and no maximum dissociation set of a tree. We present a linear time recognition algorithm which can determine whether a given vertex in a tree is contained in all (or no) maximum dissociation sets of the tree. Thus for a tree with $ n $ vertices, we can find all vertices belonging to all (or no) maximum dissociation sets of the tree in $ O(n^2) $ time.</p></abstract>

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.

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 Deception through Half-Truths

2020 ◽  
Vol 34 (06) ◽  
pp. 10110-10117
Author(s):  
Andrew Estornell ◽  
Sanmay Das ◽  
Yevgeniy Vorobeychik
Keyword(s):  
Polynomial Time ◽  
Transition Function ◽  
Np Hard ◽  
Fundamental Issue ◽  
Fake News ◽  
False Information ◽  
Important Special Case ◽  
Bayes Network ◽  
Special Case

Deception is a fundamental issue across a diverse array of settings, from cybersecurity, where decoys (e.g., honeypots) are an important tool, to politics that can feature politically motivated “leaks” and fake news about candidates. Typical considerations of deception view it as providing false information. However, just as important but less frequently studied is a more tacit form where information is strategically hidden or leaked. We consider the problem of how much an adversary can affect a principal's decision by “half-truths”, that is, by masking or hiding bits of information, when the principal is oblivious to the presence of the adversary. The principal's problem can be modeled as one of predicting future states of variables in a dynamic Bayes network, and we show that, while theoretically the principal's decisions can be made arbitrarily bad, the optimal attack is NP-hard to approximate, even under strong assumptions favoring the attacker. However, we also describe an important special case where the dependency of future states on past states is additive, in which we can efficiently compute an approximately optimal attack. Moreover, in networks with a linear transition function we can solve the problem optimally in polynomial time.

scholarly journals Total colouring regular bipartite graphs is NP-hard

1994 ◽  
Vol 124 (1-3) ◽  
pp. 155-162 ◽  
Author(s):  
Colin J.H. McDiarmid ◽  
Abdón Sánchez-Arroyo
Keyword(s):  
Bipartite Graphs ◽  
Np Hard

scholarly journals Connectivity in Hypergraphs

2018 ◽  
Vol 61 (2) ◽  
pp. 252-271 ◽  
Author(s):  
Megan Dewar ◽  
David Pike ◽  
John Proos
Keyword(s):  
Polynomial Time ◽  
The Other ◽  
Np Hard ◽  
Vertex Connectivity ◽  
Edge Connectivity ◽  
The Relationship ◽  
Weak Edge ◽  
Edge Size

AbstractIn this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that, while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong vertex cuts remains NP-hard when restricted to hypergraphs with maximum edge size at most 3. We also discuss the relationship between strong vertex connectivity and the minimum transversal problem for hypergraphs, showing that there are classes of hypergraphs for which one of the problems is NP-hard, while the other can be solved in polynomial time.

A STUDY ON RULE EXTRACTION FROM SEVERAL COMBINED NEURAL NETWORKS

2001 ◽  
Vol 11 (03) ◽  
pp. 247-255 ◽  
Author(s):  
GUIDO BOLOGNA
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Decision Trees ◽  
Polynomial Time ◽  
Public Domain ◽  
Rule Extraction ◽  
Data Sets ◽  
Np Hard ◽  
The Public ◽  
A New Technique

The problem of rule extraction from neural networks is NP-hard. This work presents a new technique to extract "if-then-else" rules from ensembles of DIMLP neural networks. Rules are extracted in polynomial time with respect to the dimensionality of the problem, the number of examples, and the size of the resulting network. Further, the degree of matching between extracted rules and neural network responses is 100%. Ensembles of DIMLP networks were trained on four data sets in the public domain. Extracted rules were on average significantly more accurate than those extracted from C4.5 decision trees.

Sign in / Sign up

Export Citation Format

Share Document