Related papers: Parameterized Aspects of Triangle Enumeration
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Diameter -- the task of computing the length of a longest shortest path -- is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no $O(n^{1.99})$-time algorithm even in sparse graphs [Roditty and…
A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…
We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a…
The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to…
Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…
Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines.…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…