Sliding Window Temporal Graph Coloring

@inproceedings{Mertzios2019SlidingWT,
  title={Sliding Window Temporal Graph Coloring},
  author={George B. Mertzios and Hendrik Molter and Viktor Zamaraev},
  booktitle={AAAI},
  year={2019}
}
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static graphs, which often stand in stark contrast to practice where data is inherently dynamic and subject to discrete changes over time. A temporal graph is a graph whose edges are assigned a set of integer time labels, indicating at which discrete time steps the… Expand
Sliding window temporal graph coloring
TLDR
A thorough investigation of the computational complexity of this temporal coloring problem is presented, and strong computational hardness results are proved, complemented by efficient exact and approximation algorithms. Expand
D M ] 1 2 N ov 2 01 8 Sliding Window Temporal Graph Coloring ∗
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloringExpand
Temporal Vertex Cover with a Sliding Time Window
TLDR
This paper introduces and study two natural temporal extensions of the classical problem VERTEX COVER, and presents a thorough investigation of the computational complexity and approximability of these two temporal covering problems. Expand
Temporal vertex cover with a sliding time window
TLDR
This paper introduces and study two natural temporal extensions of the classical problem VERTEX COVER and presents a thorough investigation of the computational complexity and approximability of these two temporal covering problems. Expand
Computing Maximum Matchings in Temporal Graphs
TLDR
This paper introduces and studies the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs, and proves strong computational hardness results for Maximum Temporal Matching. Expand
Time Complexity Analysis of Randomized Search Heuristics for the Dynamic Graph Coloring Problem
TLDR
It is shown that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time, and tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient. Expand
Runtime analysis of randomized search heuristics for dynamic graph coloring
TLDR
Borders show that reoptimization is faster than optimizing from scratch, and how to speed up computations by using problem specific operators concentrating on parts of the graph where changes have occurred is shown. Expand
The complexity of finding small separators in temporal graphs
TLDR
The notion of a temporal core (vertices whose incident edges change over time) is introduced and it is proved that the non-strict variant is fixed-parameter tractable when parameterized by the temporal core size, while the strict variant remains NP -complete, even for constant-size temporal cores. Expand
How fast can we reach a target vertex in stochastic temporal graphs?
TLDR
This paper thoroughly investigates the complexity of two naturally related, but fundamentally different, temporal path problems, called Minimum Arrival and Best Policy, and studies the hierarchy of models of memory-k, in an edge-centric network evolution setting. Expand
Interference-free Walks in Time: Temporally Disjoint Paths
TLDR
This work investigates the computational complexity of finding temporally disjoint paths or walks in temporal graphs and finds NP-hardness in general but also identifies natural tractable cases. Expand
...
1
2
3
...

References

SHOWING 1-10 OF 52 REFERENCES
Sliding window temporal graph coloring
TLDR
A thorough investigation of the computational complexity of this temporal coloring problem is presented, and strong computational hardness results are proved, complemented by efficient exact and approximation algorithms. Expand
On Temporal Graph Exploration
TLDR
The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk that starts at a given start node, visits all nodes of the graph, and has the smallest arrival time, and this work provides an explicit construction of temporal graphs that require \(\Theta (n^2) steps to be explored. Expand
Traveling Salesman Problems in Temporal Graphs
TLDR
It is proved that, it cannot be approximated within cn, for some constant c > 0, in general temporal graphs and within (2 − e), for every constant e >0, in the special case in which D(t) is connected for all 1 ≤ t ≤ l, both unless P = NP. Expand
The Computational Complexity of Finding Temporal Paths under Waiting Time Constraints
TLDR
It is shown that the "restless variant" of this problem becomes computationally hard even in very restrictive settings, for example, it is W[1]-hard when parameterized by the feedback vertex number or the pathwidth of the underlying graph. Expand
Multistage Vertex Cover
TLDR
The goal is to find for each layer of the temporal graph a small vertex cover and to guarantee that two vertex cover sets of every two consecutive layers differ not too much (specified by a given parameter). Expand
Channel assignment in mobile networks based on geometric prediction and random coloring
TLDR
A prediction based and a random coloring based approach are proposed to reduce the cost of coloring a graphlet and it is shown that both approaches perform better than an existing SNAP algorithm. Expand
The Complexity of Optimal Design of Temporally Connected Graphs
TLDR
The main technical result is that computing the maximum number of redundant labels is APX-hard, i.e., there is no PTAS unless P = NP, and the existence of minimal temporal designs with at least nlogn labels is shown. Expand
The Complexity of Finding Small Separators in Temporal Graphs
TLDR
It is proved that the non-strict variant is fixed-parameter tractable when parameterized by the size of the temporal core, while the strict variant remains NP-complete, even for constant-size temporal cores. Expand
Temporal Graph Classes: A View Through Temporal Separators
TLDR
This work investigates the computational complexity of separating two distinct vertices s and z by vertex deletion in a temporal graph and identifies sharp borders between tractable and intractable cases. Expand
Temporal Network Optimization Subject to Connectivity Constraints
TLDR
This work gives two efficient algorithms for computing shortest time-respecting paths on a temporal network, and proves that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Expand
...
1
2
3
4
5
...