Related papers: Depth first representations of $k^2$-trees
We present a scalable approach for range and $k$ nearest neighbor queries under computationally expensive metrics, like the continuous Fr\'echet distance on trajectory data. Based on clustering for metric indexes, we obtain a dynamic tree…
Recent work in Deep Learning has re-imagined the representation of data as functions mapping from a coordinate space to an underlying continuous signal. When such functions are approximated by neural networks this introduces a compelling…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming…
A spanning tree of a network or graph is a subgraph that connects all nodes with the least number or weight of edges. The spanning tree is one of the most straightforward techniques for network simplification and sampling, and for…
Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in…
In this paper, we propose an easily trained yet powerful representation learning approach with performance highly competitive to deep neural networks in a digital pathology image segmentation task. The method, called sparse coding driven…
The kTree problem is a special case of Subgraph Isomorphism where the pattern graph is a tree, that is, the input is an $n$-node graph $G$ and a $k$-node tree $T$, and the goal is to determine whether $G$ has a subgraph isomorphic to $T$.…
As the complexity and computational demands of deep learning models rise, the need for effective optimization methods for neural network designs becomes paramount. This work introduces an innovative search mechanism for automatically…
Real-world point sets tend to be clustered, so using a machine word for each point is wasteful. In this paper we first show how a compact representation of quadtrees using $\Oh{1}$ bits per node can break this bound on clustered point sets,…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
The hierarchical matrix framework partitions matrices into subblocks that are either small or of low numerical rank, enabling linear storage complexity and efficient matrix-vector multiplication. This work focuses on the $H^2$-matrix format…
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…
Stereo matching is the key step in estimating depth from two or more images. Recently, some tree-based non-local stereo matching methods have been proposed, which achieved state-of-the-art performance. The algorithms employed some tree…
Listing k-cliques plays a fundamental role in various data mining tasks, such as community detection and mining of cohesive substructures. Existing algorithms for the k-clique listing problem are built upon a general framework, which finds…
Zero-suppressed Binary Decision Diagrams (ZDDs) are data structures for representing set families in a compressed form. With ZDDs, many valuable operations on set families can be done in time polynomial in ZDD size. In some cases, however,…
Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations…
This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown…
Finding a suitable data representation for a specific task has been shown to be crucial in many applications. The success of subspace clustering depends on the assumption that the data can be separated into different subspaces. However,…
Subgraph matching is a fundamental building block for graph-based applications and is challenging due to its high-order combinatorial nature. Existing studies usually tackle it by combinatorial optimization or learning-based methods.…