A matching cut is a matching that is also an edge cut. In the problem Minimum Matching Cut, we ask for a matching cut with the minimum number of edges in the matching. We give polynomial-time algorithms for P7-free, S...
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A graph property is elusive (or evasive) if any algorithm testing it by asking questions of the form "Is there an edge between vertices x and y?" must, in the worst case, examine all pairs of vertices. Elusi...
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We investigate the problem of sybil (fake account) detection in social networks from a graph algorithms perspective, where graph structural information is used to classify users as sybil and benign. We introduce the n...
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Typical LiDAR SLAM architectures feature a front-end for odometry estimation and a back-end for refining and optimizing the trajectory and map, commonly through loop closures. However, loop closure detection in large-...
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The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many centra...
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The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and exponential improvements over the state of the art have been achieved for the runtimes of many algorithms. Nevertheless, there are still large gaps between the best known upper and lower bounds for many important problems. The current lower bound techniques for deterministic algorithms are often tailored to obtaining a logarithmic bound and essentially cannot be used to prove lower bounds beyond Ω(log n). In contrast, the best deterministic upper bounds, usually obtained via network decomposition or rounding approaches, are often polylogarithmic, raising the fundamental question of how to resolve the gap between logarithmic lower and polylogarithmic upper bounds and finally obtain tight bounds. We develop a novel algorithm design technique aimed at closing this gap. It ensures a logarithmic runtime by carefully combining local solutions into a globally feasible solution. In essence, each node finds a carefully chosen local solution in O(log n) rounds and we guarantee that this solution is consistent with the other nodes' solutions without coordination. The local solutions are based on a distributed version of Hall's theorem that may be of independent interest and motivates the title of this work. We showcase our framework by improving on the state of the art for the following fundamental problems: edge coloring, bipartite saturating matchings and hypergraph sinkless orientation (which is a generalization of the well-studied sinkless orientation problem). For each of the problems we improve the runtime for general graphs and provide asymptotically optimal algorithms for bounded degree graphs. In particular, we obtain an asymptotically optimal O(log n)-round algorithm for (3∆/2)-edge coloring in bounded degree graphs. The previously best bo
Partitioning nodes of a graph into clusters according to their simi- larities can be a very useful but complex task of data analysis. Many dierent approaches and algorithms for this problem exist, one of the possibili...
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Partitioning nodes of a graph into clusters according to their simi- larities can be a very useful but complex task of data analysis. Many dierent approaches and algorithms for this problem exist, one of the possibilities is to utilize genetic algorithms for solving this type of task. In this work, we analyze dierent approaches to clustering in general and in the domain of graphs. Several clustering algorithms based on the concept of genetic algorithm are proposed and experimentally evaluated. A server application that contains implementations of the these algorithms was developed and is attached to this thesis.
Unit edge-length drawings, rectilinear drawings (where each edge is either a horizontal or a vertical segment), and rectangular face drawings are among the most studied subjects in graph Drawing. However, most of the ...
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A graph G is k-vertex-critical if χ(G) = k but χ(G − v) 1, H2)-free if it contains no induced subgraph isomorphic to H1 nor H2. A W4 is the graph consisting of a C4 plus an additional vertex adjacent to all the vert...
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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry ...
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