
Improved Lower Bound for Competitive Graph Exploration
We give an improved lower bound of 10/3 on the competitive ratio for the...
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Online Graph Exploration on a Restricted Graph Class: Optimal Solutions for Tadpole Graphs
We study the problem of online graph exploration on undirected graphs, w...
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Learning to Route in Similarity Graphs
Recently similarity graphs became the leading paradigm for efficient nea...
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Online Domination: The Value of Getting to Know All your Neighbors
We study the dominating set problem in an online setting. An algorithm i...
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Maximum Matchings and Minimum Blocking Sets in Θ_6Graphs
Θ_6Graphs are important geometric graphs that have many applications es...
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Maximal Exploration of Trees with EnergyConstrained Agents
We consider the problem of exploring an unknown tree with a team of k in...
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Stabilization Time in Weighted Minority Processes
A minority process in a weighted graph is a dynamically changing colorin...
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Online Graph Exploration on Trees, Unicyclic Graphs and Cactus Graphs
We study the problem of exploring all vertices of an undirected weighted graph that is initially unknown to the searcher. An edge of the graph is only revealed when the searcher visits one of its endpoints. Beginning at some start node, the searcher's goal is to visit every vertex of the graph before returning to the start node on a tour as short as possible. We prove that the Nearest Neighbor algorithm's competitive ratio on trees with n vertices is Θ(log n), i.e. no better than on general graphs. This also yields a lower bound on the quality of the Nearest Neighbor heuristic for the traveling salesperson problem on trees. Furthermore, we examine the algorithm Blocking for a range of parameters not considered previously and prove it is 3competitive on unicyclic graphs as well as 5/2+√(2)≈ 3.91competitive on cactus graphs. The bestknown lower bound for these two graph classes is 2.
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