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Article
Open AccessApproximate and Randomized Algorithms for Computing a Second Hamiltonian Cycle
In this paper we consider the following problem: Given a Hamiltonian graph G, and a Hamiltonian cycle C of G, can we compute a second Hamiltonian cycle ...
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Article
Equitable scheduling on a single machine
We introduce a natural but seemingly yet unstudied variant of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. The novelty of our new variant lies in simultaneousl...
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Chapter and Conference Paper
Payment Scheduling in the Interval Debt Model
The networks-based study of financial systems has received considerable attention in recent years, but seldom explicitly incorporated the dynamic aspects of such systems. We consider this problem setting from ...
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Article
Interference-free walks in time: temporally disjoint paths
We investigate the computational complexity of finding temporally disjoint paths and walks in temporal graphs. There, the edge set changes over discrete time steps. Temporal paths and walks use edges that appear ...
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Chapter and Conference Paper
The Complexity of Growing a Graph
We study a new algorithmic process of graph growth. The process starts from a single initial vertex \(u_0\) and operates in discrete time...
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Article
Open AccessThe Power of Linear-Time Data Reduction for Maximum Matching
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in \(O(m\sqrt{n})\) O ( m n )
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Article
When Can Graph Hyperbolicity be Computed in Linear Time?
Hyperbolicity is a distance-based measure of how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unf...
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Article
Open AccessBinary Search in Graphs Revisited
In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been...
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Article
Open AccessTemporal Network Optimization Subject to Connectivity Constraints
In this work we consider temporal networks, i.e. networks defined by a labeling \(\lambda \) ...
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Chapter and Conference Paper
The Temporal Explorer Who Returns to the Base
In this paper we study the problem of exploring a temporal graph (i.e. a graph that changes over time), in the fundamental case where the underlying static graph is a star on n vertices. The aim of the exploratio...
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Chapter and Conference Paper
Kernelization Lower Bounds for Finding Constant-Size Subgraphs
Kernelization is an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such t...
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Article
Open AccessThe Complexity of Optimal Design of Temporally Connected Graphs
We study the design of small cost temporally connected graphs, under various constraints. We mainly consider undirected graphs of n vertices, where each edge has an associated set of discrete availability instanc...
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Article
Online Regenerator Placement
Connections between nodes in optical networks are realized by lightpaths. Due to the decay of the signal, a regenerator has to be placed on every lightpath after at most d hops, for some given positive integer d....
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Article
Identification, Location-Domination and Metric Dimension on Interval and Permutation Graphs. II. Algorithms and Complexity
We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets (denoted Identifying Code, (Open) Open Locating-Dominating Set and Metric Dimension) of an interva...
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Article
Determining majority in networks with local interactions and very small local memory
We study the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may later change into other types, out of a set of a...
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Chapter and Conference Paper
Population Protocols for Majority in Arbitrary Networks
We study the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may have a few additional possible states and can in...
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Chapter and Conference Paper
When Can Graph Hyperbolicity Be Computed in Linear Time?
Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last...
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Reference Work Entry In depth
Multitolerance Graphs
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Chapter and Conference Paper
Graph Editing to a Given Degree Sequence
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence where the aim is to obtain a graph with a given degree sequence
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Article
Open AccessAlgorithms and Almost Tight Results for \(3\) -Colorability of Small Diameter Graphs
The \(3\) 3 ...
