Related papers: Identifying Codes Kernelization Limitations
This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink…
The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2)…
Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…
In this paper, we study two generalizations of Vertex Cover and Edge Cover, namely Colorful Vertex Cover and Colorful Edge Cover. In the Colorful Vertex Cover problem, given an $n$-vertex edge-colored graph $G$ with colors from $\{1,…
In 2005, Goddard, Hedetniemi, Hedetniemi and Laskar [Generalized subgraph-restricted matchings in graphs, Discrete Mathematics, 293 (2005) 129 - 138] asked the computational complexity of determining the maximum cardinality of a matching…
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…
In Correlation Clustering, the input is a graph $G=(V,E)$ with weight function $\omega: {V \choose 2}\to Z$ and the task is to partition the vertex set into clusters such that the total weight of edges between clusters and missing edges…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
This paper is devoted to a study of single-peakedness on arbitrary graphs. Given a collection of preferences (rankings of a set of alternatives), we aim at determining a connected graph G on which the preferences are single-peaked, in the…
We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that…
We propose a preprocessing algorithm for the multiway cut problem that establishes its polynomial kernelizability when the difference between the parameter $k$ and the size of the smallest isolating cut is at most $log(k)$. To the best of…
We study the kernel complexity of constraint satisfaction problems over a finite domain, parameterized by the number of variables, whose constraint language consists of two relations: the non-equality relation and an additional…
Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…
The length of an optimal scalar linear index code of a groupcast index coding problem is equal to the minrank of its side information hypergraph. The side-information hypergraph becomes a side-information graph for a special class of…
A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…
Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous…
In this work, we present a concatenated repetition-polar coding scheme that is aimed at applications requiring highly unbalanced unequal bit-error protection, such as the Beam Interlock System of the Large Hadron Collider at CERN. Even…
In Computer Vision, problem of identifying or classifying the objects present in an image is called Object Categorization. It is a challenging problem, especially when the images have clutter background, occlusions or different lighting…
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…
A proper vertex coloring of a graph is said to be locally identifying if the sets of colors in the closed neighborhood of any two adjacent non-twin vertices are distinct. The lid-chromatic number of a graph is the minimum number of colors…