Related papers: Preprocessing to Reduce the Search Space: Antler S…
In parameterized complexity, it is well-known that a parameterized problem is fixed-parameter tractable if and only if it has a kernel - an instance equivalent to the input instance, whose size is just a function of the parameter. The size…
Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into…
Data collected at very frequent intervals is usually extremely sparse and has no structure that is exploitable by modern tensor decomposition algorithms. Thus the utility of such tensors is low, in terms of the amount of interpretable and…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
Kernelization is the standard framework to analyze preprocessing routines mathematically. Here, in terms of efficiency, we demand the preprocessing routine to run in time polynomial in the input size. However, today, various NP-complete…
Graph transformers have gained popularity in various graph-based tasks by addressing challenges faced by traditional Graph Neural Networks. However, the quadratic complexity of self-attention operations and the extensive layering in graph…
Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a…
The (\textsc{Weighted}) \textsc{Subset Feedback Vertex Set} problem is a generalization of the classical \textsc{Feedback Vertex Set} problem and asks for a vertex set of minimum (weighted) size that intersects all cycles containing a…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
Pre-trained Transformer language models (LM) have become go-to text representation encoders. Prior research fine-tunes deep LMs to encode text sequences such as sentences and passages into single dense vector representations for efficient…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
The Feedback vertex set with the minimum size is one of Karp's 21 NP-complete problems targeted at breaking all the cycles in a graph. This problem is applicable to a broad variety of domains, including E-commerce networks, database…
While next-token prediction (NTP) has been the standard objective for training language models, it often struggles to capture global structure in reasoning tasks. Multi-token prediction (MTP) has recently emerged as a promising alternative,…
An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these…
One of the strongest signals for automated matching of knowledge graphs and ontologies are textual concept descriptions. With the rise of transformer-based language models, text comparison based on meaning (rather than lexical features) is…
The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…
Graph Neural Networks (GNNs) are powerful tools for learning from graph-structured data, but their scalability is increasingly strained by the size of real-world graphs in domains like recommender systems, fraud detection, and molecular…
This article presents a unique design for a parser using the Ant Colony Optimization algorithm. The paper implements the intuitive thought process of human mind through the activities of artificial ants. The scheme presented here uses a…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…