# Multistage Problems on a Global Budget

@article{Heeger2021MultistagePO, title={Multistage Problems on a Global Budget}, author={Klaus Heeger and Anne-Sophie Himmel and Frank Kammer and Rolf Niedermeier and Malte Renken and Andrej Sajenko}, journal={Theor. Comput. Sci.}, year={2021}, volume={868}, pages={46-64} }

Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one studies the different (time) layers of a temporal graph (effectively meaning that the edge set may change over time, but the vertex set remains unchanged), and one searches for a solution of a given graph problem for each layer. The twist in the multistage… Expand

#### 8 Citations

A Multistage View on 2-Satisfiability

- Computer Science, Mathematics
- CIAC
- 2021

It is proved that Multistage 2-SAT is NP-hard even in quite restricted cases and parameterized algorithms for Multistages are presented and proved to be asymptotically optimal. Expand

Comparing temporal graphs using dynamic time warping

- Computer Science
- Social Network Analysis and Mining
- 2020

This work defines the dynamic temporal graph warping (dtgw) distance to determine the dissimilarity of two temporal graphs and develops a quadratic programming formulation and an efficient heuristic. Expand

Approximating Multistage Matching Problems

- Computer Science
- IWOCA
- 2021

It is shown that multistage perfect matching problems are NP-hard even in very restricted scenarios, and new approximation algorithms and methods are proposed to transfer results between different problem variants without loosing approximation guarantees. Expand

Comparing Temporal Graphs Using Dynamic Time Warping

- Computer Science, Mathematics
- COMPLEX NETWORKS
- 2019

This work defines the dynamic temporal graph warping distance (dtgw) to determine the (dis)similarity of two temporal graphs and develops an efficient heuristic which performs well in empirical studies and performs favorably in de-anonymizing networks. Expand

Broadening the Research Agenda for Computational Social Choice: Multiple Preference Profiles and Multiple Solutions

- Computer Science
- AAMAS
- 2021

This work systematically review different types of arising settings, point out how classical problems and solution concepts can be generalized, and identify several research challenges. Expand

A Faster Parameterized Algorithm for Temporal Matching

- Mathematics, Computer Science
- ArXiv
- 2020

An improved algorithm is shown to compute a $\Delta$-temporal matching of maximum size with a running time of $Delta^{O(\nu)}\cdot |\mathcal G|$ and hence provide an exponential speedup in terms of $\Delta$. Expand

FPT-space Graph Kernelizations

- Computer Science, Mathematics
- ArXiv
- 2020

The authors' kernelization for Feedback Vertex Set computes in a first step an approximated solution, which can be used to build a simple algorithm for undirected $s$-$t$-connectivity that runs in polynomial time and with $O(\mathrm{poly}(k) \log n)$ bits. Expand

Multistage s-t Path: Confronting Similarity with Dissimilarity

- Computer Science, Mathematics
- ISAAC
- 2020

It is proved that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting the W[1]-hardness proof of the corresponding similarity case. Expand

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