In a (parameterized) graph edge modification problem, we are given G, an integer k and (usually well-structured) class $$\mathcal {G}$$ of graphs, asked whether it is possible to transform G into $$G' \in \mathcal by adding and/or removing at most edges. Parameterized problems received considerable attention in the last decades. this paper, focus on finding small kernels for problems. One studi...

The survey is a comprehensive overview of the developing area parameterized algorithms for graph modification problems. It describes state art in kernelization, subexponential algorithms, and complexity modification. main focus on edge problems, where task to change some adjacencies satisfy required properties. To facilitate further research, we list many open problems area.

The design of correct topological modeling operations is known to be a time-consuming and challenging task. However, these are intuitively understood via simple drawings representative object before after modification. We propose infer from an application example. Our algorithm exploits compact expressive graph-based language. In this framework, on generalized maps represented as rules the theo...

We consider a probabilistic model for the Steiner Tree problem. Under this model the problem is defined in a 2-stage setting over a first-stage complete weighted graph having its vertices associated with a probability of presence (independently each from another) in the second stage. A first-stage feasible solution on the input graph might become infeasible in the second stage, when certain ver...

Bulk Synchronous Parallelism (BSP) provides a good model for parallel processing of many large-scale graph applications, however it is unsuitable/inefficient for graph applications that require coordination, such as graph-coloring, subcoloring, and clustering. To address this problem, we present an efficient modification to the BSP model to implement serializability (sequential consistency) wit...

We introduce overlap cluster graph modification problems where, other than in most previous work, the clusters of the target graph may overlap. More precisely, the studied graph problems ask for a minimum number of edge modifications such that the resulting graph consists of clusters (maximal cliques) that may overlap up to a certain amount specified by the overlap number s. In the case of s-ve...