Approximation algorithms for Hamming clustering problems

Approximation Algorithms for Hamming Clustering Problems

We study Hamming versions of two classical clustering problems. The Hamming radius p-clustering problem (HRC) for a set S of k binary strings, each of length n, is to find p binary strings of length n that minimize the maximum Hamming distance between a string in S and the closest of the p strings; this minimum value is termed the p-radius of S and is denoted by %. The related Hamming diameter ...

Approximation Algorithms for Clustering Problems

Approximation Algorithms for Bi-clustering Problems

One of the main goals in the analysis of microarray data is to identify groups of genes and groups of experimental conditions (including environments, individuals, and tissues) that exhibit similar expression patterns. This is the so-called biclustering problem. In this paper, we consider two variations of the biclustering problem: the consensus submatrix problem and the bottleneck submatrix pr...

Approximation Algorithms for Clustering

Approximation Algorithms for Clustering Clustering items into groups is a fundamental problem in the information sciences. Many typical clustering optimization problems are NP-hard and so cannot be expected to be solved optimally in a reasonable amount of time. Although the use of heuristics is common, in this dissertation we seek approximation algorithms, whose performance ratio in relation to...

Approximation Algorithms for Clustering Problems with Lower Bounds and Outliers

We consider clustering problems with non-uniform lower bounds and outliers, and obtain the first approximation guarantees for these problems. We have a setF of facilities with lower bounds {Li}i∈F and a setD of clients located in a common metric space {c(i, j)}i,j∈F∪D, and bounds k, m. A feasible solution is a pair ( S ⊆ F , σ : D 7→ S ∪ {out} ) , where σ specifies the client assignments, such ...