Randomized Algorithms for Some Clustering Problems

2018 ◽  
pp. 109-119 ◽  
Author(s):  
Alexander Kel’manov ◽  
Vladimir Khandeev ◽  
Anna Panasenko
Keyword(s):  
Randomized Algorithms ◽  
Clustering Problems

Combinatorial Optimization of Clustering Decisions: An Application to Refine Psychiatric Diagnoses

2018 ◽  
Author(s):  
Jordan Stevens ◽  
Douglas Steinley ◽  
Cassandra L. Boness ◽  
Timothy J Trull ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
Alcohol Use Disorder ◽  
Point Of View ◽  
Psychiatric Diagnoses ◽  
Optimal Solutions ◽  
Specific Function ◽  
Significant Information ◽  
Diagnosis Group ◽  
Clustering Problems ◽  
Unique Application

Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the diagnosis group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the diagnosis to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.

scholarly journals Linear-time approximation schemes for clustering problems in any dimensions

2010 ◽  
Vol 57 (2) ◽  
pp. 1-32 ◽  
Author(s):  
Amit Kumar ◽  
Yogish Sabharwal ◽  
Sandeep Sen
Keyword(s):  
Linear Time ◽  
Approximation Schemes ◽  
Time Approximation ◽  
Clustering Problems

scholarly journals Clustering problems in optimization models

1996 ◽  
Vol 9 (3) ◽  
pp. 229-239 ◽  
Author(s):  
Santosh Kabadi ◽  
Katta G. Murty ◽  
Cosimo Spera
Keyword(s):  
Optimization Models ◽  
Clustering Problems

GEOMETRIC ALGORITHMS FOR THE CONSTRAINED 1-D K-MEANS CLUSTERING PROBLEMS AND IMRT APPLICATIONS

2009 ◽  
Vol 20 (02) ◽  
pp. 361-377
Author(s):  
DANNY Z. CHEN ◽  
MARK A. HEALY ◽  
CHAO WANG ◽  
BIN XU
Keyword(s):  
Radiation Therapy ◽  
Treatment Planning ◽  
Intensity Modulated Radiation Therapy ◽  
Geometric Algorithms ◽  
Maximum Difference ◽  
Continuous Version ◽  
Heuristic Approaches ◽  
Clustering Problem ◽  
Intensity Modulated ◽  
Clustering Problems

In this paper, we present efficient geometric algorithms for the discrete constrained 1-D K-means clustering problem and extend our solutions to the continuous version of the problem. One key clustering constraint we consider is that the maximum difference in each cluster cannot be larger than a given threshold. These constrained 1-D K-means clustering problems appear in various applications, especially in intensity-modulated radiation therapy (IMRT). Our algorithms improve the efficiency and accuracy of the heuristic approaches used in clinical IMRT treatment planning.

PERMUTATION ROUTING AND SORTING ON THE RECONFIGURABLE MESH

1998 ◽  
Vol 09 (02) ◽  
pp. 199-211
Author(s):  
SANGUTHEVAR RAJASEKARAN ◽  
THEODORE MCKENDALL
Keyword(s):  
Lower Bound ◽  
Randomized Algorithms ◽  
Linear Array ◽  
Order Term ◽  
Routing Algorithm ◽  
Sorting Algorithm ◽  
Routing Problem ◽  
Reconfigurable Mesh ◽  
Permutation Routing ◽  
Time Bounds

In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation which we call as Mr. We also make use of the standard PARBUS model. We show that permutation routing problem can be solved on a linear array Mr of size n in [Formula: see text] steps, whereas n-1 is the best possible run time without reconfiguration. A trivial lower bound for routing on Mr will be [Formula: see text]. On the PARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal. We also show that permutation routing on an n×n reconfigurable mesh Mr can be done in time n+o(n) using a randomized algorithm or in time 1.25n+o(n) deterministically. In contrast, 2n-2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n-2 steps on a conventional mesh. A lower bound of [Formula: see text] is in effect for routing on the 2D mesh Mr as well. On the other hand, n is a lower bound for routing on the PARBUS and our algorithms have the same time bounds on the PARBUS as well. Thus our randomized routing algorithm is optimal upto a lower order term. In addition we show that the problem of sorting can be solved in randomized time n+o(n) on Mr as well as on PARBUS. Clearly, this sorting algorithm will be optimal on the PARBUS model. The time bounds of our randomized algorithms hold with high probability.

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