Scholarship & Research
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Item Computing a consensus trajectory in a vehicular network(Springer Science and Business Media LLC, 2022-09) Zou, Peng; Qingge, Letu; Yang, Qing; Zhu, BinhaiIn this paper, we study the problem of computing a consensus trajectory of a vehicle given the history of Points of Interest visited by the vehicle over a certain period of time. The problem arises when a system tries to establish the social connection between two vehicles in a vehicular network, where three versions of the problem are studied. Formally, given a set of m trajectories, the first version of the problem is to compute a target (median) sequence T over Σ such that the sum of similarity measure (i.e., number of adjacencies) between T and all Si’s is maximized. For this version, we show that the problem is NP-hard and we present a simple factor-2 approximation based on a greedy method. We implement the greedy algorithm and a variation of it which is based on a more natural greedy search on a new data structure called adjacency map. In the second version of the problem where the sequence T is restricted to be a permutation, we show that the problem remains NP-hard but the approximation factor can be improved to 1.5. In the third version where the sequence T has to contain all letters of Σ, we again prove that it is NP-hard. We implement a simple greedy algorithm and a variation of the 1.5-approximation algorithm for the second version, and which are used to construct solution for the third version. Our algorithms are tested on the simulation data and the empirical results are very promising.Item Computational investigation on protein sequencing and genome rearrangement problems(Montana State University - Bozeman, College of Engineering, 2018) Qingge, Letu; Chairperson, Graduate Committee: Binhai ZhuDe novo protein sequencing and genome rearrangement problems are the classical problems in bioinformatics. De novo protein sequencing problem try to determine the whole sequence of amino acids based on the mass spectrometry data without using the database search. Genome rearrangement problems try to recognize the evolutionary process between two species. In this dissertation, first, we describe the process of constructing target protein sequences by utilizing mass spectrometry based data from both top-down and bottom-up tandem mass spectra. In addition to using data from mass spectrometry analysis, we also utilize techniques for de novo protein sequencing using a homologous protein sequence as a reference to attempt to fill in any remaining gaps in the constructed protein scaffold. Initial results for analysis on real datasets yield over 96-100% coverage and 73-91% accuracy with the target protein sequence. Second, we use different genome rearrangement operations to transform one genome to another such that the similarity between two genomes is maximized. We explore these problems in terms of theoretical and experimental analysis. For sorting unsigned genome problem by double cut and join (DCJ) operation, we design a randomized fixed parameter tractable (FPT) approximation algorithm for computing the DCJ distance with an approximation factor 4/3 + Epsilon, and the running time O*(2 d*), where d* represents the optimal DCJ distance. For one-sided exemplar adjacency number problem, we reformulate the problem as maximum independent set in a colored interval graph and hence reduce the appearance of each gene at most twice. Moreover, we design a factor-2 approximation and also show that the approximation factor can not be improved less than 2 by some local search technique. At last, we apply integer linear programming to solve the reduced instance exactly. For the minimum copy number generation problem, we analyze the complexity of different variations of this problem and show a practical algorithm for the general case based on greedy method.Item Optimizing Cyclist Parking in a Closed System(Montana State University, 2016-10) Qingge, Letu; Smith, KillianIn this paper, we consider the two different aspects of the bike parking problem; namely the assignment of bike racks to locations, and the selection of the minimal number of bike rack locations satisfying some maximum walking distanced. The first sub-problem considered was the assignment of bike racks to individual buildings in the attempt to satisfy the needs of the total number of cyclists expected to reside within a building during the course of an average day. We show that the case of assigning a finite number of bike racks to all buildings on a campus is NP-Hard, and propose a greedy algorithm to obtain a solution. The case of allowing for additional bike racks to be purchased is shown to bePolynomial-Time solvable. The second sub-problem, finding the minimal number of bike rack locations, is shown to be NP-Hard, and a method to use approximation algorithms for the Maximum Independent Set to find solutions is demonstrated.