Related papers: Soft and Constrained Hypertree Width

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

Segmentation evaluation metrics traditionally rely on binary decision logic: predictions are either correct or incorrect, based on rigid IoU thresholds. Detection--based metrics such as F1 and mAP determine correctness at the object level…

A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper,…

Hyperdimensional Computing (HDC) is emerging as a promising approach for edge AI, offering a balance between accuracy and efficiency. However, current HDC-based applications often rely on high-precision models and/or encoding matrices to…

We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…

In this paper, we propose a new Soft Confidence-Weighted (SCW) online learning scheme, which enables the conventional confidence-weighted learning method to handle non-separable cases. Unlike the previous confidence-weighted learning…

Decision trees are widely adopted machine learning models due to their simplicity and explainability. However, as training data size grows, standard methods become increasingly slow, scaling polynomially with the number of training…

Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091--3120, 2010], the Zhang--Shu framework has attracted extensive attention and motivated many bound-preserving (BP) high-order discontinuous Galerkin and finite volume…

It is known for many algorithmic problems that if a tree decomposition of width $t$ is given in the input, then the problem can be solved with exponential dependence on $t$. A line of research by Lokshtanov, Marx, and Saurabh [SODA 2011]…

The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large…

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…

Width-based planning methods deal with conjunctive goals by decomposing problems into subproblems of low width. Algorithms like SIW thus fail when the goal is not easily serializable in this way or when some of the subproblems have a high…

In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed…

Sparse structures are frequently sought when pursuing tractability in optimization problems. They are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present.…

Learning discriminative representations is a central goal of supervised deep learning. While cross-entropy (CE) remains the dominant objective for classification, it does not explicitly enforce desirable geometric properties in the…

We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…

Existing compression methods typically focus on the removal of signal-level redundancies, while the potential and versatility of decomposing visual data into compact conceptual components still lack further study. To this end, we propose a…

Model compression has been introduced to reduce the required hardware resources while maintaining the model accuracy. Lots of techniques for model compression, such as pruning, quantization, and low-rank approximation, have been suggested…

A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization, i.e., a cycle-free realization of the code on the…

We propose a new methodology to develop heuristic algorithms using tree decompositions. Traditionally, such algorithms construct an optimal solution of the given problem instance through a dynamic programming approach. We modify this…