<p>U sklopu doktorske disertacije izvršeno je istraživanje vezano za automatsko<br />raspoređivanje elemenata dijagrama. Kroz analizu postojećih rešenja uočen je<br />prostor za poboljšanja, posebno po pitanju raznovrsnosti dostupnih algoritama<br />i pomoći korisniku pri izboru najpogodnijeg od njih. U okviru istraživanja<br />proučavan, implementiran i u pojedinim slučajevima unapređen je širok<br />spektar algoritama za crtanje i analizu grafova. Definisan je postupak<br />automatskog izbora odgovarajućeg algoritma za raspoređivanje elemenata<br />grafova na osnovu njihovih osobina. Dodatno, osmišljen je jezik specifičan za<br />domen koji korisnicima grafičkih editora pruža pomoć u izboru algoritma za<br />raspoređivanje, a programerima brže pisanje koda za poziv željenog algoritma.</p> / <p>This thesis presents a research aimed towards the problem of automatically<br />laying out elements of a diagram. The analysis of existing solutions showed that there<br />is some room for improvement, especially regarding variety of available algorithms.<br />Also, none of the solutions offer possibility of automatically choosing an appropriate<br />graph layout algorithm. Within the research, a large number of different algorithms for<br />graph drawing and analysis were studied, implemented, and, in some cases,<br />enhanced. A method for automatically choosing the best available layout algorithm<br />based on properties of a graph was defined. Additionally, a domain-specific language<br />for specifying a graph&rsquo;s layout was designed.</p>

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: p. 212-214. / by Robert Hunter Halstead, Jr. / Ph.D.

程序員常利用現有的應用程序介面建立新程序，但遇到的困難是花很多時間去找尋并學習適當的應用程序介面 [8]。在這篇論文中，我們提出新方向幫助對某應用程序介面比較陌生的程序員：以短語搜尋應用程序介面連通子圖。我們以一大圖表達應用程序介面的調用，當用家提交一組文字短語后，便能從這大圖中找出一個符合需要的最理想連通子圖。 / 這新方向的挑戰是簡單的子圖搜尋需要很大的搜尋空間。我們提出兩組機制改良了一套現有的貪婪子圖搜尋算法，以此找出一個其節點與搜尋短語的文字相近的連通子圖。另外，這套現有的貪婪子圖搜尋算法需要很短的圖節點之間的最短路徑計算時間，我們提出了一套空間效率高的索引，能較快的找出節點間的精確最短路徑。從實驗中，我們通過兩組現實生活中的搜尋數據比較了此新方法與一最新式的程序碼建議方法Portfolio [19]，發現兩組數據的平均F₁-Measure能分別有效地提高了64%與36%。 / Reusing APIs of existing libraries is a common practice during software development, but searching suitable APIs and their usages can be time-consuming [8]. There have been studies to help users nd usages of APIs given names of functions. In this paper, we study a new and more practical approach to help users nd usages of APIs given only simple text phrases expressed in natural language, when users have limited knowledge about an API library. We model API invocations as an API graph and aim to nd an optimum connected subgraph that meets users’ search needs. / The problem is challenging since the search space in an API graph is very huge. We start with a greedy subgraph search algorithm which returns a connected subgraph containing nodes with high textual similarity to the query phrases. Two renement techniques are proposed to improve the quality of the returned subgraph. Furthermore, as the greedy subgraph search algorithm relies on online query of shortest path between two graph nodes, we propose a space-effcient compressed shortest path indexing scheme that can eciently recover the exact shortest path. We conduct extensive experiments to show that the proposed subgraph search approach for API recommendation is very eective in that it boosts the average F₁-measure of the state-of-the-art approach, Portfolio [19], on two groups of real-life queries by 64% and 36% respectively. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chan, Wing Kwan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 59-62). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation & Challenges --- p.2 / Chapter 1.2 --- Contributions --- p.4 / Chapter 1.3 --- Organization of Thesis --- p.5 / Chapter 2 --- Related Works --- p.7 / Chapter 2.1 --- Keyword Search in Graphs --- p.7 / Chapter 2.2 --- Team Formation in Expert Network --- p.8 / Chapter 2.3 --- API/Code Recommendation --- p.10 / Chapter 3 --- Problem Statement & Proposed Approach --- p.12 / Chapter 3.1 --- Problem Statement --- p.12 / Chapter 3.2 --- API Subgraph Search --- p.15 / Chapter 3.2.1 --- A Greedy Subgraph Search Algorithm --- p.16 / Chapter 3.2.2 --- Selecting Node with High Textual Similarity --- p.19 / Chapter 3.2.3 --- Handling Multiple Shortest Paths Problem --- p.21 / Chapter 3.2.4 --- Time Complexity --- p.24 / Chapter 3.2.5 --- Approximation Ratio --- p.25 / Chapter 3.3 --- Class-Only Path Indexing --- p.25 / Chapter 3.3.1 --- Three Indexing Structures --- p.27 / Chapter 3.3.2 --- Exact Path Recovery --- p.28 / Chapter 3.3.3 --- Space Complexity --- p.30 / Chapter 3.4 --- Alternative Approaches --- p.31 / Chapter 3.4.1 --- Enhanced Steiner Tree --- p.31 / Chapter 3.4.2 --- Finding R-clique --- p.32 / Chapter 4 --- Experiments --- p.35 / Chapter 4.1 --- Effectiveness - Among Subgraph Searching Algorithms --- p.35 / Chapter 4.1.1 --- Dataset --- p.35 / Chapter 4.1.2 --- Results --- p.36 / Chapter 4.2 --- Effectiveness - Between Two API Recommendations --- p.38 / Chapter 4.2.1 --- Query Formulation --- p.39 / Chapter 4.2.2 --- Results --- p.41 / Chapter 4.3 --- Effciency - Runtime --- p.44 / Chapter 4.4 --- Indexing Comparison Class Graph Vs. Full Graph --- p.46 / Chapter 4.4.1 --- Runtime & Memory --- p.46 / Chapter 4.4.2 --- Gain Score --- p.48 / Chapter 4.5 --- A Comparison with Finding R-Clique --- p.49 / Chapter 4.6 --- Threats to Validity --- p.50 / Chapter 5 --- Conclusion & Future Works --- p.55 / Chapter 5.1 --- Conclusion --- p.55 / Chapter 5.2 --- Future Works --- p.56 / Bibliography --- p.59

No description available.

图结构能够描述数据对象之间的复杂关系，因而被广泛应用于多种领域。随着相关应用领域的发展，图数据库的规模变得庞大且仍在不断增长。这给研究者在图查询和图挖掘方面带来新的挑战。本文主要研究以下三个问题：如何确定两个图的顶点对应关系，使得其中一个图的子结构匹配到另一个图的相似子结构；如何从含有多个小图的数据库中，找到与查询图相似的图；如何在由不同类别的图组成的数据库中，选取特征子图并对图进行分类。 / 在本文中，对于第一个问题，我们提出了新的两段式图匹配算法。在第一阶段，我们采用了一个新的启发式策略，能够先选取锚顶点并向外扩展，进而快速得到初始匹配。在第二阶段，我们设计了新的算法对初始匹配加以改进，并且证明了新的匹配优于初始匹配。这个两段式图匹配算法能够快速有效地获得两个图的高质量匹配。为解决第二个问题，我们首先定义一个新的度量以衡量两图间的距离。它基于两图间的最大公共子图，能够很好地捕捉两个图的相同及不同之处。由于最大公共子图的计算是NP完全问题，为了快速回答top-k相似图查询，我们提出了一个高效算法，能够极大地减少最大公共子图的计算次数。这个算法根据距离度量的三种下界进行剪枝以筛选掉不合格的图。其中，前两种下界的计算基于两图的结构信息，第三种下界可由距离度量的三角不等式性质推出。我们还设计了三种不同的索引结构来支持剪枝，它们能够在剪枝效果和索引时间方面达到不同程度的平衡。关于第三个问题，我们发现了目前广泛使用的特征判别函数的两个主要缺陷，并据此提出了一个新的多样性特征判别函数。它不仅能衡量特征的判别性，而且能衡量特征的多样性。我们从多个方面分析了这个函数的性质，发现它能更好地区分不同类别的图。基于这个函数，我们设计了新的特征选取算法，获得很高的分类精度。 / Graph has powerful ability to model complex structural relationships among data objects and has been widely used in various applications. Along with the development of the application domains, graph databases become large and are growing rapidly in size. This brings researchers new challenges on graph query and mining, among which we mainly focus on investigating the following three problems: how to find the correspondence between the nodes of two large graphs so that some substructures in one graph are mapped to similar substructures in the other; another problem is how to retrieve similar graphs for a query graph from a graph database consisting of a large number of graphs; and the last problem is how to extract subgraph features to build an automated classification model for a graph database containing graphs which belong to different classes. / In this thesis, for the first problem, we propose a novel two-step approach which can efficiently match two large graphs over thousands of nodes with high matching quality. In the first stage, we design an anchor-selection/expansion scheme to construct a good initial matching heuristically. In the second stage, we propose a new approach to refine the initial matching and give the optimality of our refinement algorithm. Our approach can produce an approximate matching result with high quality and efficiency. To address the second problem, we introduce a new graph distance measure based on the maximum common subgraphs (MCS) of two graphs which can thoroughly capture the common as well as different structures of two graphs. Since computing the MCS of two graphs is NP-complete, to answer the top-k graph similarity query efficiently, we propose a fast algorithm which can significantly reduce the number of MCS computations. This algorithm prunes the unqualified graphs based on three lower bounds in which the first two are derived based on the structures of two graphs and the third is obtained based on the triangle property of the distance measure. Three index schemes are designed with different tradeoffs between pruning power and construction cost to assist the query processing. For the third problem, we identify two main issues of the current widely-used discriminative score for feature selection, and introduce a new diversified discriminative score to explore the additional value of the diversity together with the discriminativity. We analyze the properties of the newly-proposed diversified discriminative score from several perspectives and demonstrate that this score can make positive/negative graphs more separable. New algorithms are also proposed to select features based on the new score and they are shown to have high classification accuracy. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhu, Yuanyuan. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 137-146). / Abstract also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.iii / Acknowledgments --- p.iv / Contents --- p.vi / List of Tables --- p.x / List of Figures --- p.xi / Notations --- p.1 / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Motivation --- p.2 / Chapter 1.1.1. --- Large Graph Matching --- p.3 / Chapter 1.1.2. --- Top-k Graph Similarity Query --- p.4 / Chapter 1.1.3. --- Diversified Discriminative Feature Selection --- p.6 / Chapter 1.2. --- Contribution --- p.7 / Chapter 2. --- Preliminaries --- p.10 / Chapter 3. --- Related Work --- p.16 / Chapter 3.1. --- Graph Matching --- p.16 / Chapter 3.1.1. --- Exact Graph Matching --- p.16 / Chapter 3.1.2. --- Approximate Graph Matching --- p.17 / Chapter 3.2. --- Graph Similarity Query --- p.19 / Chapter 3.3. --- Graph Classification --- p.20 / Chapter 4. --- Large Graph Matching --- p.23 / Chapter 4.1. --- Problem Statement --- p.23 / Chapter 4.2. --- An Overview: Construction and Refinement --- p.24 / Chapter 4.3. --- Matching Construction --- p.26 / Chapter 4.3.1. --- Global and Local Node Similarity --- p.26 / Chapter 4.3.2. --- Anchor Selection and Expansion --- p.33 / Chapter 4.3.3. --- Discussion on τ for Anchor Selection --- p.36 / Chapter 4.4. --- Matching Refinement --- p.39 / Chapter 4.4.1. --- Vertex Cover Based Refinement --- p.39 / Chapter 4.4.2. --- Refinement and Its Optimality --- p.41 / Chapter 4.4.3. --- Randomly Refinement Excluding C - F₁ --- p.46 / Chapter 4.4.4. --- Randomly Refinement Including C - F₁ --- p.51 / Chapter 4.5. --- Labeled Graph Handling --- p.54 / Chapter 4.6. --- Experiments --- p.56 / Chapter 4.6.1. --- Comparison with the Approximate Algorithms --- p.59 / Chapter 4.6.2. --- Comparison with the Exact Algorithm --- p.63 / Chapter 4.6.3. --- Parameter and Scalability Testing --- p.65 / Chapter 4.6.4. --- Sensitivity of Randomness (PN) --- p.69 / Chapter 4.6.5. --- Effectiveness of Label Distribution --- p.70 / Chapter 4.7. --- Summary --- p.72 / Chapter 5. --- Top-k Graph Similarity Query --- p.73 / Chapter 5.1. --- Problem Statement --- p.73 / Chapter 5.2. --- The Framework --- p.78 / Chapter 5.3. --- Pruning without Indexing --- p.80 / Chapter 5.3.1. --- Edge Frequency Based Lower Bound --- p.80 / Chapter 5.3.2. --- Adjacency List Based Lower Bound --- p.82 / Chapter 5.3.3. --- Query Processing --- p.84 / Chapter 5.4. --- Pruning with Indexing --- p.85 / Chapter 5.4.1. --- The Triangle Property of Graph Distance --- p.86 / Chapter 5.4.2. --- Query Processing --- p.88 / Chapter 5.4.3. --- Indexing --- p.92 / Chapter 5.4.4. --- Discussion on the Generality of Our Framework --- p.94 / Chapter 5.5. --- Experiments --- p.94 / Chapter 5.5.1. --- Similarity Measures Evaluation --- p.96 / Chapter 5.5.2. --- Query Performance Evaluation --- p.98 / Chapter 5.5.3. --- Indexing Cost Evaluation --- p.102 / Chapter 5.6. --- Summary --- p.103 / Chapter 6. --- Diversified Discriminative Feature Selection --- p.105 / Chapter 6.1. --- Problem Statement --- p.105 / Chapter 6.2. --- Discriminative Score --- p.108 / Chapter 6.2.1. --- The Single Feature Discriminative Score --- p.109 / Chapter 6.2.2. --- A New Diversified Discriminative Score --- p.110 / Chapter 6.3. --- Property Statistics of Discriminative Score --- p.113 / Chapter 6.4. --- The Algorithms --- p.117 / Chapter 6.5. --- Ensemble D&D --- p.121 / Chapter 6.6. --- Experiments --- p.123 / Chapter 6.6.1. --- D&D Performance Analysis --- p.126 / Chapter 6.6.2. --- Comparison with Existing Algorithms --- p.127 / Chapter 6.6.3. --- Performance on Patterns Mined by GAIA --- p.129 / Chapter 6.7. --- Summary --- p.131 / Chapter 7. --- Conclusion and FutureWork --- p.132 / Chapter 7.1. --- Conclusion --- p.132 / Chapter 7.2. --- Future work --- p.134 / Bibliography --- p.136

由于现今在各个领域涌现的图数据规模都愈加庞大，在这些大规模图数据上进行任何一种简单的查询都成为一件有富有挑战性的工作。在本文中，我们着重在大规模图上研究三个具有广泛应用的查询：最短路查询，权重限制查询和最近k关键字查询。具体来说， 最短路查询是一个计算两点间最短距离的基本查询。而权重限制查询判断两点间是否存在一条沿路边权都满足用指定条件的可行路径。对于一个查询节点，最近k关键字查询返回k个距离最近的带有指定关键字的节点。在面对一个拥有超过一亿节点的图时，我们需要为这些查询开发有效的索引和查询优化算法。 / 在本文中，对于最短路查询，我们提出了两个基于地标嵌入的算法，一个是有误差控制的地标嵌入算法，另一个则是本地化地标嵌入算法。前者通过对地标的筛选和组织，能对估计的最短距离给予一定的误差保证； 而后者提出的本地化机制能够在不增加预处理复杂度和在线查询复杂度的情况下大幅度提高估计的精准度。对于权重限制查询，我们先提出一个能够保证常数查询时间的内存算法。除此之外，为了提高算法对大规模数据的处理能力，我们使用编码技术设计了一个有效的外存算法。对于最近k关键字查询，我们先在一个特殊的图，即一颗树上，开发一个有效算法来在常数时间内回答最近k关键字查询， 并由此得出一个图上的近似算法；此外我们还通过一个全局存储的技术来进一步减少索引大小和缩短查询时间。我们在真实和模拟的数据上做了大量的实验，实验结果证明我们的算法在大图上对上述三个查询都具有高效性能。 / Due to the massive size of graphs from various domains nowadays, even simple graph queries become challenging tasks. In this thesis, three queries with a wide range of applications are investigated on large graphs. One is shortest distance query, a fundamental query which computes the shortest distance between two nodes. Another query, weight constraint reachability (WCR), checks if there is a feasible path between two nodes where edge weights along the path satisfy a side constraint. And the third one, a top-k nearest keywords (k-NK) query, reports, for a query node, the k nearest nodes bearing some user-specified keywords. When confronting with a large-scale graph with over tens of millions of nodes, we need to develop efficient indexing and query optimization techniques for these queries. / In this thesis, for a shortest distance query, we devise two landmark embedding schemes, an error bounded landmark scheme and a local landmark scheme, where the former can guarantee an error bound for estimated distance, and the latter can significantly improve the distance estimation accuracy without increasing the offline embedding or the online query complexity. For a WCR query, we propose a memorybased approach which promises a constant query time. Besides, in order to increase its scalability, we devise an I/O-efficient approach for answering a WCR query on massive graphs. For a k-NK query, we start with a special case when the graph is a tree, based on which we present our algorithm for approximate k-NK query on a graph. A global storage technique is devised to further reduce the index size and the query time. We did extensive experiments on the three queries respectively to show the effectiveness and efficiency of our methods. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Qiao, Miao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 141-151). / Abstract also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgements --- p.iii / Contents --- p.v / Chapter 1. --- Introduction --- p.1 / Chapter 1.1. --- Motivation --- p.1 / Chapter 1.1.1. --- Shortest Distance Query --- p.1 / Chapter 1.1.2. --- Weight Constraint Reachability Query --- p.4 / Chapter 1.1.3. --- Top-k Nearest Keyword Query --- p.7 / Chapter 1.2. --- Contributions --- p.9 / Chapter 1.3. --- Roadmap --- p.11 / Chapter 2. --- RelatedWork --- p.12 / Chapter 2.1. --- Shortest Distance Query --- p.12 / Chapter 2.2. --- Reachability Query --- p.14 / Chapter 2.3. --- Keyword Related Query --- p.15 / Chapter 3. --- Querying Shortest Distance --- p.17 / Chapter 3.1. --- Landmark Embedding --- p.17 / Chapter 3.2. --- Error Bounded Landmark Scheme --- p.18 / Chapter 3.2.1. --- Problem Statement --- p.18 / Chapter 3.2.2. --- Proposed Algorithm --- p.18 / Chapter 3.2.3. --- Graph Partitioning-based Heuristic --- p.22 / Chapter 3.2.4. --- Experiments --- p.27 / Chapter 3.3. --- Query-Dependent Local Landmark Scheme --- p.34 / Chapter 3.3.1. --- Problem Statement --- p.34 / Chapter 3.3.2. --- Shortest Path Tree Based Local Landmark --- p.37 / Chapter 3.3.3. --- Optimization Techniques --- p.41 / Chapter 3.3.4. --- Local Landmark Scheme on Relational Database --- p.48 / Chapter 3.3.5. --- Experiment --- p.56 / Chapter 3.4. --- Summary --- p.64 / Chapter 4. --- QueryingWeight Constraint Reachability --- p.65 / Chapter 4.1. --- Problem Definition --- p.65 / Chapter 4.1.1. --- Edge Weight Constraint --- p.65 / Chapter 4.1.2. --- Node Weight Constraint --- p.66 / Chapter 4.1.3. --- Two Basic Solutions --- p.67 / Chapter 4.2. --- An Efficient Memory Algorithm --- p.68 / Chapter 4.2.1. --- Properties of WCR --- p.68 / Chapter 4.2.2. --- Novel Edge Based Indexing --- p.70 / Chapter 4.2.3. --- Extension to Other Constraint Formats --- p.76 / Chapter 4.3. --- An I/O-Efficient Index --- p.77 / Chapter 4.3.1. --- Vertex Coding --- p.78 / Chapter 4.3.2. --- MST Re-balancing --- p.80 / Chapter 4.3.3. --- Disk-Based Index Construction --- p.84 / Chapter 4.3.4. --- Query Processing --- p.85 / Chapter 4.4. --- Experiments --- p.87 / Chapter 4.5. --- Summary --- p.101 / Chapter 5. --- Querying Top K-Nearest Keyword --- p.102 / Chapter 5.1. --- Problem Definition --- p.102 / Chapter 5.2. --- Existing Solutions --- p.103 / Chapter 5.2.1. --- Approximate k-NK on a Graph --- p.104 / Chapter 5.2.2. --- Exact 1-NK on a Tree --- p.106 / Chapter 5.3. --- Solution Overview --- p.108 / Chapter 5.4. --- K-NK on a Tree for a Small K --- p.110 / Chapter 5.4.1. --- Query Processing --- p.110 / Chapter 5.4.2. --- Construction of Entry Edge Partition --- p.115 / Chapter 5.4.3. --- Construction of Candidate List --- p.118 / Chapter 5.5. --- K-NK on a Tree for a Large K --- p.120 / Chapter 5.5.1. --- A Basic Pivot Approach --- p.121 / Chapter 5.5.2. --- Pivot Approach with Tree Balancing --- p.122 / Chapter 5.5.3. --- Index Construction --- p.125 / Chapter 5.6. --- Approximate K-NK on a Graph --- p.128 / Chapter 5.7. --- Experiments --- p.133 / Chapter 5.8. --- Summary --- p.138 / Chapter 6. --- Conclusions and Future Work --- p.139 / Bibliography --- p.140

by Ng Suk Fung. / "February 18, 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 215-222). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Graph-structured data is enjoying an increasing popularity among Web technology and new data management and archiving techniques. Numerous applications work with graphs and need to query reachability among nodes in graphs. A 2-hop cover can compactly represent the whole edge transitive closure of a graph in O ( / Cheng, Jiefeng. / "August 2007." / Adviser: Jeffrey Xu Yu. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1097. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 134-141). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

In this dissertation, we develop frequent free tree mining systems, F3TM and CFFTree, to systematically discover the complete set of (closed) frequent free trees from a graph database. Graph indexing, another problem addressed in this dissertation, is of special interest both in academia and in industrial applications. The solutions, (Tree+Delta ) and SimTree, propose a free tree featured index, which is built on frequent free tree patterns discovered through a structural mining process. This mining-based indexing methodology leads to the development of a compact but effective graph index structure that is orders of magnitude smaller in size but an order of magnitude faster in performance than traditional approaches. / Scalable structural pattern mining and graph database management tools become increasingly crucial to applications with complex data in domains ranging from software engineering to computational biology. Due to their high complexity, it is often difficult, if not impossible, for human beings to manually analyze any reasonably large collection of graphs. In this dissertation, we investigate two fundamental problems in large scale graph databases: Given a graph database what are the hidden free tree patterns and how can we find them? And how can we index graphs based on free tree patterns and perform similarity search in large graph databases? / The developed concepts, theories, and systems hence increase our understanding of data mining principles in structural pattern discovery, interpretation and search. The formulation of a general free tree featured graph information system through this study could provide fundamental supports to graph-intensive applications. / Zhao, Peixiang. / "August 2007." / Adviser: Jeffrey Xu Yu. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1127. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 136-145). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Rectilinear Steiner minimum tree (RSMT) problem asks for a shortest tree spanning a set of given terminals using only horizontal and vertical lines. Construction of RSMTs is an important problem in VLSI physical design. It is useful for both the detailed and global routing steps, and it is important for congestion, wire length and timing estimations during the floorplanning or placement step. The original RSMT problem assumes no obstacle in the routing region. However, in today’s designs, there can be many routing blockages, like macro cells, IP blocks and pre-routed nets. Therefore, the RSMT problem with blockages has become an important problem in practice and has received a lot of research attentions in the recent years. The RSMT problem has been shown to be NP-complete, and the introduction of obstacles has made this problem even more complicated. / In the first part of this thesis, we propose an exact algorithm, called ObSteiner, for the construction of obstacle-avoiding RSMT (OARSMT) in the presence of complex rectilinear obstacles. Our work is developed based on the GeoSteiner approach in which full Steiner trees (FSTs) are first constructed and then combined into a RSMT. We modify and extend the algorithm to allow rectilinear obstacles in the routing region. We prove that by adding virtual terminals to each routing obstacle, the FSTs in the presence of obstacles will follow some very simple structures. A two-phase approach is then developed for the construction of OARSMTs. In the first phase, we generate a set of FSTs. In the second phase, the FSTs generated in the first phase are used to construct an OARSMT. Experimental results show that ObSteiner is able to handle problems with hundreds of terminals in the presence of up to two thousand obstacles, generating an optimal solution in a reasonable amount of time. / In the second part of this thesis, we propose the OARSMT problem with slew constraints over obstacles. In modern VLSI designs, obstacles usually block a fraction of metal layers only making it possible to route over the obstacles. However, since buffers cannot be place on top of any obstacle, we should avoid routing long wires over obstacles. Therefore, we impose the slew constraints for the interconnects that are routed over obstacles. To deal with this problem, we analyze the optimal solutions and prove that the internal trees with signal direction over an obstacle will follow some simple structures. Based on this observation, we propose an exact algorithm, called ObSteiner with slew constraints, that is able to find an optimal solution in the extended Hanan grid. Experimental results show that the proposed algorithm is able to reduce nearly 5% routing resources on average in comparison with the OARSMT algorithm and is also very much faster. / Huang, Tao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves [137]-144). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The rectilinear Steiner minimum tree problem --- p.1 / Chapter 1.2 --- Applications --- p.3 / Chapter 1.3 --- Obstacle consideration --- p.5 / Chapter 1.4 --- Thesis outline --- p.6 / Chapter 1.5 --- Thesis contributions --- p.8 / Chapter 2 --- Background --- p.11 / Chapter 2.1 --- RSMT algorithms --- p.11 / Chapter 2.1.1 --- Heuristics --- p.11 / Chapter 2.1.2 --- Exact algorithms --- p.20 / Chapter 2.2 --- OARSMT algorithms --- p.30 / Chapter 2.2.1 --- Heuristics --- p.30 / Chapter 2.2.2 --- Exact algorithms --- p.33 / Chapter 3 --- ObSteiner - an exact OARSMT algorithm --- p.37 / Chapter 3.1 --- Introduction --- p.38 / Chapter 3.2 --- Preliminaries --- p.39 / Chapter 3.2.1 --- OARSMT problem formulation --- p.39 / Chapter 3.2.2 --- An exact RSMT algorithm --- p.40 / Chapter 3.3 --- OARSMT decomposition --- p.42 / Chapter 3.3.1 --- Full Steiner trees among complex obstacles --- p.42 / Chapter 3.3.2 --- More Theoretical results --- p.59 / Chapter 3.4 --- OARSMT construction --- p.62 / Chapter 3.4.1 --- FST generation --- p.62 / Chapter 3.4.2 --- Pruning of FSTs --- p.66 / Chapter 3.4.3 --- FST concatenation --- p.71 / Chapter 3.5 --- Incremental construction --- p.82 / Chapter 3.6 --- Experiments --- p.83 / Chapter 4 --- ObSteiner with slew constraints --- p.97 / Chapter 4.1 --- Introduction --- p.97 / Chapter 4.2 --- Problem Formulation --- p.100 / Chapter 4.3 --- Overview of our approach --- p.103 / Chapter 4.4 --- Internal tree structures in an optimal solution --- p.103 / Chapter 4.5 --- Algorithm --- p.126 / Chapter 4.5.1 --- EFST and SCIFST generation --- p.127 / Chapter 4.5.2 --- Concatenation --- p.129 / Chapter 4.5.3 --- Incremental construction --- p.131 / Chapter 4.6 --- Experiments --- p.131 / Chapter 5 --- Conclusion --- p.135 / Bibliography --- p.137