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In this paper, we study the problem of graph similarity search with graph edit distance (GED) constraints. Due to the NP-hardness of GED computation, existing solutions to this problem adopt the filtering-and-verification framework with a…
Graph similarity computation (GSC) is to calculate the similarity between one pair of graphs, which is a fundamental problem with fruitful applications in the graph community. In GSC, graph edit distance (GED) and maximum common subgraph…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Despite the efficacy of graph-based algorithms for Approximate Nearest Neighbor (ANN) searches, the optimal tuning of such systems remains unclear. This study introduces a method to tune the performance of off-the-shelf graph-based indexes,…
There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this…
Near neighbor search (NNS) is a powerful abstraction for data access; however, data indexing is troublesome even for approximate indexes. For intrinsically high-dimensional data, high-quality fast searches demand either indexes with…
Edge-labeled graphs are widely used to describe relationships between entities in a database. Given a query subgraph that represents an example of what the user is searching for, we study the problem of efficiently searching for similar…
Quantifying the semantic similarity between database queries is a critical challenge with broad applications, ranging from query log analysis to automated educational assessment of SQL skills. Traditional methods often rely solely on…
In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub…
Recently, graph query is widely adopted for querying knowledge graphs. Given a query graph $G_Q$, the graph query finds subgraphs in a knowledge graph $G$ that exactly or approximately match $G_Q$. We face two challenges on graph query: (1)…
Agentic retrieval improves multi-hop question answering by giving language models autonomy to iteratively gather evidence. Recent work augments these systems with knowledge graphs for structured traversal, but this combination introduces…
Graphs are ubiquitous real-world data structures, and generative models that approximate distributions over graphs and derive new samples from them have significant importance. Among the known challenges in graph generation tasks,…
Important data mining problems such as nearest-neighbor search and clustering admit theoretical guarantees when restricted to objects embedded in a metric space. Graphs are ubiquitous, and clustering and classification over graphs arise in…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
As techniques for graph query processing mature, the need for optimization is increasingly becoming an imperative. Indices are one of the key ingredients toward efficient query processing strategies via cost-based optimization. Due to the…
Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…
Nearest neighbor search and k-nearest neighbor graph construction are two fundamental issues arise from many disciplines such as multimedia information retrieval, data-mining and machine learning. They become more and more imminent given…
Semi-structured knowledge bases (SKBs) embed textual documents in a typed graph of entities and relations, and underpin applications such as product search, academic paper search, and precision-medicine inquiries. Existing hybrid retrieval…
Finding locally optimal solutions for max-cut and max-$k$-cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…