Related papers: Explicit linear kernels for packing problems

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…

The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base…

We investigate a fundamental vertex-deletion problem called (Induced) Subgraph Hitting: given a graph $G$ and a set $\mathcal{F}$ of forbidden graphs, the goal is to compute a minimum-sized set $S$ of vertices of $G$ such that $G-S$ does…

We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these…

We investigate polynomial-time preprocessing for the problem of hitting forbidden minors in a graph, using the framework of kernelization. For a fixed finite set of connected graphs F, the F-Deletion problem is the following: given a graph…

In the $k$-Leaf Out-Branching and $k$-Internal Out-Branching problems we are given a directed graph $D$ with a designated root $r$ and a nonnegative integer $k$. The question is to determine the existence of an outbranching rooted at $r$…

In the {\sc Hitting Set} problem, we are given a collection $\cal F$ of subsets of a ground set $V$ and an integer $p$, and asked whether $V$ has a $p$-element subset that intersects each set in $\cal F$. We consider two parameterizations…

We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total…

We give the first linear kernels for the (Connected) Dominating Set problems on H-topological minor free graphs. We prove the existence of polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph. The problem is known to be fixed-parameter tractable (FPT), and is unlikely to have a polynomial sized kernel (under complexity…

For a (possibly infinite) fixed family of graphs F, we say that a graph G overlays F on a hypergraph H if V(H) is equal to V(G) and the subgraph of G induced by every hyperedge of H contains some member of F as a spanning subgraph.While it…

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

The \textsc{$l$-Exact Component Order Connectivity} problem asks whether, given an input graph $G$ and an integer $k$, there exists a vertex subset $S\subseteq V(G)$ of size at most $k$ such that every connected component in $G - S$ has…

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…

We consider the problem of discovering overlapping communities in networks which we model as generalizations of Graph Packing problems with overlap. We seek a collection $\mathcal{S}' \subseteq \mathcal{S}$ consisting of at least $k$ sets…

Given a family $\mathcal{F}$ of graphs, a graph is \emph{$\mathcal{F}$-subgraph-free} if it has no subgraph isomorphic to a member of $\mathcal{F}$. We present a fixed-parameter linear-time algorithm that decides whether a planar graph can…

We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…

Motivated by chemical applications, we revisit and extend a family of positive definite kernels for graphs based on the detection of common subtrees, initially proposed by Ramon et al. (2003). We propose new kernels with a parameter to…