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Network Analysis: Methodological Foundations
TLDR
This paper presents a meta-modelling system that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually calculating centrality indices.
The complexity of path coloring and call scheduling
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Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs
TLDR
This work presents the first constant-factor approximation algorithm for the minimum-weight dominating set problem in unit disk graphs, a problem motivated by applications in wireless ad-hoc networks.
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Network Analysis: Methodological Foundations (Lecture Notes in Computer Science)
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
TLDR
These are the first known PTASs for $\mathcal{NP}$-hard optimization problems on disk graphs based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible.
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Optimal bandwidth reservation in hose-model VPNs with multi-path routing
TLDR
This work demonstrates that the use of multipath routing offers significant advantages in bandwidth provisioning for VPNs and presents an optimal polynomial-time algorithm that computes a bandwidth reservation of minimum cost using multi-path routing.
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Polynomial-time approximation schemes for geometric graphs
TLDR
These are the first known polynomial-time approximation schemes for NP-hard optimization problems on disk graphs based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible.
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Length-bounded cuts and flows
TLDR
It is shown that in graphs with unit-capacities and general edge lengths it is <i>NP</i>-complete to decide whether there is a fractional length-bounded flow of a given value.
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Approximating geometric coverage problems
TLDR
This study uses the well-known (unit) disk model for wireless networks and shows that Unique Coverage remains NP-hard in this case and presents a polynomial-time 1/18-approximation algorithm for the minimum membership set cover problem.
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Broadcast scheduling: Algorithms and complexity
TLDR
A proof that FIFO is a 2-competitive online algorithm for minimizing the maximum response time and that there is no better deterministic online algorithm are given.
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