
FineGrained Completeness for Optimization in P
We initiate the study of finegrained completeness theorems for exact an...
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Fast Sequence Segmentation using LogLinear Models
Sequence segmentation is a wellstudied problem, where given a sequence ...
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Kernel Clustering with Sigmoidbased Regularization for Efficient Segmentation of Sequential Data
Kernel segmentation aims at partitioning a data sequence into several no...
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Efficient PTAS for the Maximum Traveling Salesman Problem in a Metric Space of Fixed Doubling Dimension
The maximum traveling salesman problem (Max TSP) is one of the intensive...
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A PolynomialTime Approximation Scheme for Facility Location on Planar Graphs
We consider the classic Facility Location problem on planar graphs (non...
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Sequence Modeling via Segmentations
Segmental structure is a common pattern in many types of sequences such ...
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Minimum Segmentation for Pangenomic Founder Reconstruction in Optimal Time
Given a threshold L and a set R = {R_1, ..., R_m} of m haplotype sequenc...
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Strongly polynomial efficient approximation scheme for segmentation
Partitioning a sequence of length n into k coherent segments is one of the classic optimization problems. As long as the optimization criterion is additive, the problem can be solved exactly in O(n^2k) time using a classic dynamic program. Due to the quadratic term, computing the exact segmentation may be too expensive for long sequences, which has led to development of approximate solutions. We consider an existing estimation scheme that computes (1 + ϵ) approximation in polylogarithmic time. We augment this algorithm, making it strongly polynomial. We do this by first solving a slightly different segmentation problem, where the quality of the segmentation is the maximum penalty of an individual segment. By using this solution to initialize the estimation scheme, we are able to obtain a strongly polynomial algorithm. In addition, we consider a cumulative version of the problem, where we are asked to discover the optimal segmentation for each prefix of the input sequence. We propose a strongly polynomial algorithm that yields (1 + ϵ) approximation in O(nk^2 / ϵ) time. Finally, we consider a cumulative version of the maximum segmentation, and show that this can be solved in O(nk k) time.
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