Packing Cars into Narrow Roads: PTASs for Limited Supply Highway

In the Highway problem, we are given a path with n edges (the highway), and a set of m drivers, each one characterized by a subpath and a budget. For a given assignment of edge prices (the tolls), the highway owner collects from each driver the total price of the associated path when it does not exceed drivers\u27s budget, and zero otherwise. The goal is to choose the prices to maximize the total profit. A PTAS is known for this (strongly NP-hard) problem [Grandoni,Rothvoss-SODA\u2711, SICOMP\u2716]. In this paper we study the limited supply generalization of Highway, that incorporates capacity constraints. Here the input also includes a capacity u_e >= 0 for each edge e; we need to select, among drivers that can afford the required price, a subset such that the number of drivers that use each edge e is at most u_e (and we get profit only from selected drivers). To the best of our knowledge, the only approximation algorithm known for this problem is a folklore O(log m) approximation based on a reduction to the related Unsplittable Flow on a Path problem (UFP). The main result of this paper is a PTAS for limited supply highway. As a second contribution, we study a natural generalization of the problem where each driver i demands a different amount d_i of capacity. Using known techniques, it is not hard to derive a QPTAS for this problem. Here we present a PTAS for the case that drivers have uniform budgets. Finding a PTAS for non-uniform-demand limited supply highway is left as a challenging open problem

Prizing on Paths: A PTAS for the Highway Problem

In the highway problem, we are given an n-edge line graph (the highway), and a set of paths (the drivers), each one with its own budget. For a given assignment of edge weights (the tolls), the highway owner collects from each driver the weight of the associated path, when it does not exceed the budget of the driver, and zero otherwise. The goal is choosing weights so as to maximize the profit. A lot of research has been devoted to this apparently simple problem. The highway problem was shown to be strongly NP-hard only recently [Elbassioni,Raman,Ray-'09]. The best-known approximation is O(\log n/\log\log n) [Gamzu,Segev-'10], which improves on the previous-best O(\log n) approximation [Balcan,Blum-'06]. In this paper we present a PTAS for the highway problem, hence closing the complexity status of the problem. Our result is based on a novel randomized dissection approach, which has some points in common with Arora's quadtree dissection for Euclidean network design [Arora-'98]. The basic idea is enclosing the highway in a bounding path, such that both the size of the bounding path and the position of the highway in it are random variables. Then we consider a recursive O(1)-ary dissection of the bounding path, in subpaths of uniform optimal weight. Since the optimal weights are unknown, we construct the dissection in a bottom-up fashion via dynamic programming, while computing the approximate solution at the same time. Our algorithm can be easily derandomized. We demonstrate the versatility of our technique by presenting PTASs for two variants of the highway problem: the tollbooth problem with a constant number of leaves and the maximum-feasibility subsystem problem on interval matrices. In both cases the previous best approximation factors are polylogarithmic [Gamzu,Segev-'10,Elbassioni,Raman,Ray,Sitters-'09]

Developing graph-based co-scheduling algorithms on multicore computers

It is common that multiple cores reside on the same chip and share the on-chip cache. As a result, resource sharing can cause performance degradation of co-running jobs.Job co-scheduling is a technique that can effectively alleviate this contention and many co-schedulers have been reported in related literature. Most solutions however do not aim to find the optimal co-scheduling solution. Being able to determine the optimal solution is critical for evaluating co-scheduling systems. Moreover, most co-schedulers only consider serial jobs, and there often exist both parallel and serial jobs in real-world systems. In this paper a graph-based method is developed to find the optimal co-scheduling solution for serial jobs; the method is then extended to incorporate parallel jobs, including multi-process, and multithreaded parallel jobs. A number of optimization measures are also developed to accelerate the solving process. Moreover, a flexible approximation technique is proposed to strike a balance between the solving speed and the solution quality. Extensive experiments are conducted to evaluate the effectiveness of the proposed co-scheduling algorithms. The results show that the proposed algorithms can find the optimal co-scheduling solution for both serial and parallel jobs. The proposed approximation technique is also shown to be flexible in the sense that we can control the solving speed by setting the requirement for the solution quality

Assembly of long error-prone reads using de Bruijn graphs

The recent breakthroughs in assembling long error-prone reads were based on the overlap-layout-consensus (OLC) approach and did not utilize the strengths of the alternative de Bruijn graph approach to genome assembly. Moreover, these studies often assume that applications of the de Bruijn graph approach are limited to short and accurate reads and that the OLC approach is the only practical paradigm for assembling long error-prone reads. We show how to generalize de Bruijn graphs for assembling long error-prone reads and describe the ABruijn assembler, which combines the de Bruijn graph and the OLC approaches and results in accurate genome reconstructions

Safety in multi-assembly via paths appearing in all path covers of a DAG

Peer reviewe

Safety in multi-assembly via paths appearing in all path covers of a DAG

Peer reviewe

RNA 상호작용 및 DNA 서열의 정보해독을 위한 기계학습 기법

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 김선.생물체 간 표현형의 차이는 각 개체의 유전적 정보 차이로부터 기인한다. 유전적 정보의 변화에 따라서, 각 생물체는 서로 다른 종으로 진화하기도 하고, 같은 병에 걸린 환자라도 서로 다른 예후를 보이기도 한다. 이처럼 중요한 생물학적 정보는 대용량 시퀀싱 분석 기법 등을 통해 다양한 오믹스 데이터로 측정된다. 그러나, 오믹스 데이터는 고차원 특징 및 소규모 표본 데이터이기 때문에, 오믹스 데이터로부터 생물학적 정보를 해석하는 것은 매우 어려운 문제이다. 일반적으로, 데이터 특징의 개수가 샘플의 개수보다 많을 때, 오믹스 데이터의 해석을 가장 난해한 기계학습 문제들 중 하나로 만듭니다. 본 박사학위 논문은 기계학습 기법을 활용하여 고차원적인 생물학적 데이터로부터 생물학적 정보를 추출하기 위한 새로운 생물정보학 방법들을 고안하는 것을 목표로 한다. 첫 번째 연구는 DNA 서열을 활용하여 종 간 비교와 동시에 DNA 서열상에 있는 다양한 지역에 담긴 생물학적 정보를 유전적 관점에서 해석해보고자 하였다. 이를 위해, 순위 기반 k 단어 문자열 비교방법, RKSS 커널을 개발하여 다양한 게놈 상의 지역에서 여러 종 간 비교 실험을 수행하였다. RKSS 커널은 기존의 k 단어 문자열 커널을 확장한 것으로, k 길이 단어의 순위 정보와 종 간 공통점을 표현하는 비교기준점 개념을 활용하였다. k 단어 문자열 커널은 k의 길이에 따라 단어 수가 급증하지만, 비교기준점은 극소수의 단어로 이루어져 있으므로 서열 간 유사도를 계산하는 데 필요한 계산량을 효율적으로 줄일 수 있다. 게놈 상의 세 지역에 대해서 실험을 진행한 결과, RKSS 커널은 기존의 커널에 비해 종 간 유사도 및 차이를 효율적으로 계산할 수 있었다. 또한, RKSS 커널은 실험에 사용된 생물학적 지역에 포함된 생물학적 정보량 차이를 생물학적 지식과 부합되는 순서로 비교할 수 있었다. 두 번째 연구는 생물학적 네트워크를 통해 복잡하게 얽힌 유전자 상호작용 간 정보를 해석하여, 더 나아가 생물학적 기능 해석을 통해 암의 아형을 분류하고자 하였다. 이를 위해, 그래프 컨볼루션 네트워크와 어텐션 메커니즘을 활용하여 패스웨이 기반 해석 가능한 암 아형 분류 모델(GCN+MAE)을 고안하였다. 그래프 컨볼루션 네트워크를 통해서 생물학적 사전 지식인 패스웨이 정보를 학습하여 복잡한 유전자 상호작용 정보를 효율적으로 다루었다. 또한, 여러 패스웨이 정보를 어텐션 메커니즘을 통해 해석 가능한 수준으로 병합하였다. 마지막으로, 학습한 패스웨이 레벨 정보를 보다 복잡하고 다양한 유전자 레벨로 효율적으로 전달하기 위해서 네트워크 전파 알고리즘을 활용하였다. 다섯 개의 암 데이터에 대해 GCN+MAE 모델을 적용한 결과, 기존의 암 아형 분류 모델들보다 나은 성능을 보였으며 암 아형 특이적인 패스웨이 및 생물학적 기능을 발굴할 수 있었다. 세 번째 연구는 패스웨이로부터 서브 패스웨이/네트워크를 찾기 위한 연구다. 패스웨이나 생물학적 네트워크에 단일 생물학적 기능이 아니라 다양한 생물학적 기능이 포함되어 있음에 주목하였다. 단일 기능을 지닌 유전자 조합을 찾기 위해서 생물학적 네트워크상에서 조건 특이적인 유전자 모듈을 찾고자 하였으며 MIDAS라는 도구를 개발하였다. 패스웨이로부터 유전자 상호작용 간 활성도를 유전자 발현량과 네트워크 구조를 통해 계산하였다. 계산된 활성도들을 활용하여 다중 클래스에서 서로 다르게 활성화된 서브 패스들을 통계적 기법에 기반하여 발굴하였다. 또한, 어텐션 메커니즘과 그래프 컨볼루션 네트워크를 통해서 해당 연구를 패스웨이보다 더 큰 생물학적 네트워크에 확장하려고 시도하였다. 유방암 데이터에 대해 실험을 진행한 결과, MIDAS와 딥러닝 모델을 다중 클래스에서 차이가 나는 유전자 모듈을 효과적으로 추출할 수 있었다. 결론적으로, 본 박사학위 논문은 DNA 서열에 담긴 진화적 정보량 비교, 패스웨이 기반 암 아형 분류, 조건 특이적인 유전자 모듈 발굴을 위한 새로운 기계학습 기법을 제안하였다.Phenotypic differences among organisms are mainly due to the difference in genetic information. As a result of genetic information modification, an organism may evolve into a different species and patients with the same disease may have different prognosis. This important biological information can be observed in the form of various omics data using high throughput instrument technologies such as sequencing instruments. However, interpretation of such omics data is challenging since omics data is with very high dimensions but with relatively small number of samples. Typically, the number of dimensions is higher than the number of samples, which makes the interpretation of omics data one of the most challenging machine learning problems. My doctoral study aims to develop new bioinformatics methods for decoding information in these high dimensional data by utilizing machine learning algorithms. The first study is to analyze the difference in the amount of information between different regions of the DNA sequence. To achieve the goal, a ranked-based k-spectrum string kernel, RKSS kernel, is developed for comparative and evolutionary comparison of various genomic region sequences among multiple species. RKSS kernel extends the existing k-spectrum string kernel by utilizing rank information of k-mers and landmarks of k-mers that represents a species. By using a landmark as a reference point for comparison, the number of k-mers needed to calculating sequence similarities is dramatically reduced. In the experiments on three different genomic regions, RKSS kernel captured more reliable distances between species according to genetic information contents of the target region. Also, RKSS kernel was able to rearrange each region to match a biological common insight. The second study aims to efficiently decode complex genetic interactions using biological networks and, then, to classify cancer subtypes by interpreting biological functions. To achieve the goal, a pathway-based deep learning model using graph convolutional network and multi-attention based ensemble (GCN+MAE) for cancer subtype classification is developed. In order to efficiently reduce the relationships between genes using pathway information, GCN+MAE is designed as an explainable deep learning structure using graph convolutional network and attention mechanism. Extracted pathway-level information of cancer subtypes is transported into gene-level again by network propagation. In the experiments of five cancer data sets, GCN+MAE showed better cancer subtype classification performances and captured subtype-specific pathways and their biological functions. The third study is to identify sub-networks of a biological pathway. The goal is to dissect a biological pathway into multiple sub-networks, each of which is to be of a single functional unit. To achieve the goal, a condition-specific sub-module detection method in a biological network, MIDAS (MIning Differentially Activated Subpaths) is developed. From the pathway, edge activities are measured by explicit gene expression and network topology. Using the activities, differentially activated subpaths are explored by a statistical approach. Also, by extending this idea on graph convolutional network, different sub-networks are highlighted by attention mechanisms. In the experiment with breast cancer data, MIDAS and the deep learning model successfully decomposed gene-level features into sub-modules of single functions. In summary, my doctoral study proposes new computational methods to compare genomic DNA sequences as information contents, to model pathway-based cancer subtype classifications and regulations, and to identify condition-specific sub-modules among multiple cancer subtypes.Chapter 1 Introduction 1 1.1 Biological questions with genetic information 2 1.1.1 Biological Sequences 2 1.1.2 Gene expression 2 1.2 Formulating computational problems for the biological questions 3 1.2.1 Decoding biological sequences by k-mer vectors 3 1.2.2 Interpretation of complex relationships between genes 7 1.3 Three computational problems for the biological questions 9 1.4 Outline of the thesis 14 Chapter 2 Ranked k-spectrum kernel for comparative and evolutionary comparison of DNA sequences 15 2.1 Motivation 16 2.1.1 String kernel for sequence comparison 17 2.1.2 Approach: RKSS kernel 19 2.2 Methods 21 2.2.1 Mapping biological sequences to k-mer space: the k-spectrum string kernel 23 2.2.2 The ranked k-spectrum string kernel with a landmark 24 2.2.3 Single landmark-based reconstruction of phylogenetic tree 27 2.2.4 Multiple landmark-based distance comparison of exons, introns, CpG islands 29 2.2.5 Sequence Data for analysis 30 2.3 Results 31 2.3.1 Reconstruction of phylogenetic tree on the exons, introns, and CpG islands 31 2.3.2 Landmark space captures the characteristics of three genomic regions 38 2.3.3 Cross-evaluation of the landmark-based feature space 45 Chapter 3 Pathway-based cancer subtype classification and interpretation by attention mechanism and network propagation 46 3.1 Motivation 47 3.2 Methods 52 3.2.1 Encoding biological prior knowledge using Graph Convolutional Network 52 3.2.2 Re-producing comprehensive biological process by Multi-Attention based Ensemble 53 3.2.3 Linking pathways and transcription factors by network propagation with permutation-based normalization 55 3.3 Results 58 3.3.1 Pathway database and cancer data set 58 3.3.2 Evaluation of individual GCN pathway models 60 3.3.3 Performance of ensemble of GCN pathway models with multi-attention 60 3.3.4 Identification of TFs as regulator of pathways and GO term analysis of TF target genes 67 Chapter 4 Detecting sub-modules in biological networks with gene expression by statistical approach and graph convolutional network 70 4.1 Motivation 70 4.1.1 Pathway based analysis of transcriptome data 71 4.1.2 Challenges and Summary of Approach 74 4.2 Methods 78 4.2.1 Convert single KEGG pathway to directed graph 79 4.2.2 Calculate edge activity for each sample 79 4.2.3 Mining differentially activated subpath among classes 80 4.2.4 Prioritizing subpaths by the permutation test 82 4.2.5 Extension: graph convolutional network and class activation map 83 4.3 Results 84 4.3.1 Identifying 36 subtype specific subpaths in breast cancer 86 4.3.2 Subpath activities have a good discrimination power for cancer subtype classification 88 4.3.3 Subpath activities have a good prognostic power for survival outcomes 90 4.3.4 Comparison with an existing tool, PATHOME 91 4.3.5 Extension: detection of subnetwork on PPI network 98 Chapter 5 Conclusions 101 국문초록 127Docto