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A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines $\ell_1$ and $\ell_2$, one on each. A bipartite permutation graph is a permutation graph which is bipartite. In the the…

Data Structures and Algorithms · Computer Science 2024-01-03 Jan Derbisz

Several algorithmic meta-theorems on kernelization have appeared in the last years, starting with the result of Bodlaender et al. [FOCS 2009] on graphs of bounded genus, then generalized by Fomin et al. [SODA 2010] to graphs excluding a…

Data Structures and Algorithms · Computer Science 2014-11-21 Valentin Garnero , Christophe Paul , Ignasi Sau , Dimitrios M. Thilikos

Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage…

Given a graph $G=(V,E)$ and a positive integer $t\geq2$, the task in the vertex cover $P_t$ ($VCP_t$) problem is to find a minimum subset of vertices $F\subseteq V$ such that every path of order $t$ in $G$ contains at least one vertex from…

Combinatorics · Mathematics 2023-06-22 Zongwen Bai , Jianhua Tu , Yongtang Shi

In the $K_t$-free edge deletion problem, the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of at most $k$ edges of $G$ whose removal results a graph with no clique of size $t$. In this paper we…

Data Structures and Algorithms · Computer Science 2019-08-13 Dekel Tsur

A complete graph is the graph in which every two vertices are adjacent. For a graph $G=(V,E)$, the complete width of $G$ is the minimum $k$ such that there exist $k$ independent sets $\mathtt{N}_i\subseteq V$, $1\le i\le k$, such that the…

Discrete Mathematics · Computer Science 2016-12-28 Van Bang Le , Sheng-Lung Peng

Given a hypergraph $H = (V,E)$, what is the smallest subset $X \subseteq V$ such that $e \cap X \neq \emptyset$ holds for all $e \in E$? This problem, known as the hitting set problem, is a basic problem in parameterized complexity theory.…

Computational Complexity · Computer Science 2018-01-03 Max Bannach , Till Tantau

The unit interval vertex deletion problem asks for a set of at most $k$ vertices whose deletion from an $n$-vertex graph makes it a unit interval graph. We develop an $O(k^4)$-vertex kernel for the problem, significantly improving the…

Data Structures and Algorithms · Computer Science 2016-07-06 Yuping Ke , Yixin Cao , Xiating Ouyang , Jianxin Wang

In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer…

Data Structures and Algorithms · Computer Science 2022-08-05 Ajinkya Gaikwad , Soumen Maity

We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size $k$ allows for algorithms in the Adjacency List (AL)…

Data Structures and Algorithms · Computer Science 2024-07-19 Jelle J. Oostveen , Erik Jan van Leeuwen

Recently, some large kernel convnets strike back with appealing performance and efficiency. However, given the square complexity of convolution, scaling up kernels can bring about an enormous amount of parameters and the proliferated…

Computer Vision and Pattern Recognition · Computer Science 2024-03-19 Honghao Chen , Xiangxiang Chu , Yongjian Ren , Xin Zhao , Kaiqi Huang

The Treewidth-2 Vertex Deletion problem asks whether a set of at most $t$ vertices can be removed from a graph, such that the resulting graph has treewidth at most two. A graph has treewidth at most two if and only if it does not contain a…

Data Structures and Algorithms · Computer Science 2022-03-21 Jeroen L. G. Schols

A graph $G$ is signed if each edge is assigned $+$ or $-$. A signed graph is balanced if there is a bipartition of its vertex set such that an edge has sign $-$ if and only if its endpoints are in different parts. The Edwards-Erd\"os bound…

Data Structures and Algorithms · Computer Science 2023-06-22 Luerbio Faria , Sulamita Klein , Ignasi Sau , Rubens Sucupira

Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…

Machine Learning · Computer Science 2021-02-10 Pouya M Ghari , Yanning Shen

In the Graph Reconstruction (GR) problem, the goal is to recover a hidden graph by utilizing some oracle that provides limited access to the structure of the graph. The interest is in characterizing how strong different oracles are when the…

Data Structures and Algorithms · Computer Science 2025-09-15 Juha Harviainen , Pekka Parviainen

The composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability…

Computational Complexity · Computer Science 2017-12-27 Till Fluschnik , Danny Hermelin , André Nichterlein , Rolf Niedermeier

The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

Machine Learning · Computer Science 2020-06-16 Brendon K. Colbert , Matthew M. Peet

A proper Helly circular-arc graph is an intersection graph of a set of arcs on a circle such that none of the arcs properly contains any other arc and every set of pairwise intersecting arcs has a common intersection. The Proper Helly…

Discrete Mathematics · Computer Science 2024-01-09 Akanksha Agrawal , Satyabrata Jana , Abhishek Sahu

For a fixed graph $H$, the $H$-free-editing problem asks whether we can modify a given graph $G$ by adding or deleting at most $k$ edges such that the resulting graph does not contain $H$ as an induced subgraph. The problem is known to be…

Combinatorics · Mathematics 2019-11-12 Eduard Eiben , William Lochet , Saket Saurabh

We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…

Machine Learning · Computer Science 2014-03-18 John Moeller , Parasaran Raman , Avishek Saha , Suresh Venkatasubramanian