Related papers: Kernelization Algorithms for Packing Problems Allo…
Partial set cover problem and set multi-cover problem are two generalizations of set cover problem. In this paper, we consider the partial set multi-cover problem which is a combination of them: given an element set $E$, a collection of…
We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (Newman and Leicht 2007…
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,…
Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…
The panoptic segmentation task requires a unified result from semantic and instance segmentation outputs that may contain overlaps. However, current studies widely ignore modeling overlaps. In this study, we aim to model overlap relations…
Kernelization algorithms, usually a preprocessing step before other more traditional algorithms, are very special in the sense that they return (reduced) instances, instead of final results. This characteristic excludes the freedom of…
The 3-\textsc{Hitting Set} problem is also called the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. In this paper, we address kernelizations of the \textsc{Vertex Cover} problem on 3-uniform hypergraphs. We show that this problem…
Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with…
Given a graph $G = (V,E)$, a threshold function $t~ :~ V \rightarrow \mathbb{N}$ and an integer $k$, we study the Harmless Set problem, where the goal is to find a subset of vertices $S \subseteq V$ of size at least $k$ such that every…
In the $(k,h)$-SetCover problem, we are given a collection $\mathcal{S}$ of sets over a universe $U$, and the goal is to distinguish between the case that $\mathcal{S}$ contains $k$ sets which cover $U$, from the case that at least $h$ sets…
We address the question of whether it may be worthwhile to convert certain, now classical, NP-complete problems to one of a smaller number of kernel NP-complete problems. In particular, we show that Karp's classical set of 21 NP-complete…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
Let $G$ be a planar graph and $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a "token" on each vertex of $I_s$ and seek to move all tokens to $I_t$, by repeated "token jumping", removing a single token from…
Various real-world problems consist of partitioning a set of locations into disjoint subsets, each subset spread in a way that it covers the whole set with a certain radius. Given a finite set S, a metric d, and a radius r, define a subset…
An {\em ordered $r$-graph} is an $r$-uniform hypergraph whose vertex set is linearly ordered. Given $2\leq k\leq r$, an ordered $r$-graph $H$ is {\em interval} $k$-{\em partite} if there exist at least $k$ disjoint intervals in the ordering…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
The {\sc $k$-Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) with at least $k$ leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized…
A parameterized problem consists of a classical problem and an additional component, the so-called parameter. This point of view allows a formal definition of preprocessing: Given a parameterized instance (I,k), a polynomial kernelization…
In this paper, the cooperative caching problem in fog radio access networks (F-RAN) is investigated. To maximize the incremental offloaded traffic, we formulate the clustering optimization problem with the consideration of cooperative…
Algorithms for detecting communities in complex networks are generally unsupervised, relying solely on the structure of the network. However, these methods can often fail to uncover meaningful groupings that reflect the underlying…