
Monitoring the edges of a graph using distances
We introduce a new graphtheoretic concept in the area of network monito...
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Cyclic Shift Problems on Graphs
We study a new reconfiguration problem inspired by classic mechanical pu...
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A Computational Approach to Organizational Structure
An organizational structure defines how an organization arranges and man...
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Parameterized complexity of reconfiguration of atoms
Our work is motivated by the challenges presented in preparing arrays of...
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Consensus under Network Interruption and Effective Resistance Interdiction
We study the problem of network robustness under consensus dynamics. We ...
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Maximal and maximum transitive relation contained in a given binary relation
We study the problem of finding a maximal transitive relation contained ...
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Hardness of Token Swapping on Trees
Given a graph where every vertex has exactly one labeled token, how can ...
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Shortest Reconfiguration of Matchings
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the distance between two token configurations (resp., the corresponding matchings), which is given by the length of a shortest transformation. We give a polynomialtime algorithm for the case that at least one of the two configurations is not inclusionwise maximal and show that otherwise, the problem admits no polynomialtime sublogarithmicfactor approximation unless P = NP. Furthermore, we show that the distance of two configurations in bipartite graphs is fixedparameter tractable parameterized by the size d of the symmetric difference of the source and target configurations, and obtain a d^εfactor approximation algorithm for every ε > 0 if additionally the configurations correspond to maximum matchings. Our two main technical tools are the EdmondsGallai decomposition and a close relation to the Directed Steiner Tree problem. Using the former, we also characterize those graphs whose corresponding configuration graphs are connected. Finally, we show that deciding if the distance between two configurations is equal to a given number ℓ is complete for the class D^P, and deciding if the diameter of the graph of configurations is equal to ℓ is D^Phard.
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