Related papers: Practical Algorithms for Finding Extremal Sets

Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…

The Tsetlin Machine (TM) offers high-speed inference on resource-constrained devices such as CPUs. Its logic-driven operations naturally lend themselves to parallel execution on modern CPU architectures. Motivated by this, we propose an…

We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…

We developed a flexible parallel algorithm for graph summarization based on vertex-centric programming and parameterized message passing. The base algorithm supports infinitely many structural graph summary models defined in a formal…

Neural architecture search (NAS), an important branch of automatic machine learning, has become an effective approach to automate the design of deep learning models. However, the major issue in NAS is how to reduce the large search time…

Processors with extensible instruction sets are often used today as programmable hardware accelerators for various domains. When extending RISC-V and other similar extensible processor architectures, the task of designing specialized…

Finding anomalous subsequence in a long time series is a very important but difficult problem. Existing state-of-the-art methods have been focusing on searching for the subsequence that is the most dissimilar to the rest of the…

Data represented as strings abounds in biology, linguistics, document mining, web search and many other fields. Such data often have a hierarchical structure, either because they were artificially designed and composed in a hierarchical…

This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a…

Approximate Nearest Neighbor Search (ANNS) is a fundamental operation in vector databases, enabling efficient similarity search in high-dimensional spaces. While dense ANNS has been optimized using specialized hardware accelerators, sparse…

Approximate Nearest Neighbor Search (ANNS) is a critical component of modern AI systems, such as recommendation engines and retrieval-augmented large language models (RAG-LLMs). However, scaling ANNS to billion-entry datasets exposes…

Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…

Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting…

A recently proposed exact algorithm for the maximum independent set problem is analyzed. The typical running time is improved exponentially in some parameter regions compared to simple binary search. The algorithm also overcomes the core…

Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…

In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…

Finding the maximum matching in bipartite graphs is a fundamental graph operation widely used in various fields. To expedite the acquisition of the maximum matching, Karp and Sipser introduced two data reduction rules aimed at decreasing…

This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum…

This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum…

We present two algorithms for the minimum feedback vertex set problem in planar graphs: an $O(n \log n)$ PTAS using a linear kernel and balanced separator, and a heuristic algorithm using kernelization and local search. We implemented these…