# On k-Path Covers and their applications

@article{Funke2015OnKC, title={On k-Path Covers and their applications}, author={Stefan Funke and Andr{\'e} Nusser and Sabine Storandt}, journal={The VLDB Journal}, year={2015}, volume={25}, pages={103-123} }

For a directed graph G with vertex set V, we call a subset $$C\subseteq V$$C⊆V a k-(All-)Path Cover if C contains a node from any simple path in G consisting of k nodes. This paper considers the problem of constructing small k-Path Covers in the context of road networks with millions of nodes and edges. In many application scenarios, the set C and its induced overlay graph constitute a very compact synopsis of G, which is the basis for the currently fastest data structure for personalized…

## Figures and Tables from this paper

## 37 Citations

Hierarchical and Dynamic k-Path Covers

- Computer ScienceCIKM
- 2016

The experiments showed that the construction algorithm can yield high solution quality, and has a short running time for large values of k, and it was verified that the dynamic algorithm can handle an edge weight change within 40 ms.

Efficient Distance Sensitivity Oracles for Real-World Graph Data

- Computer ScienceIEEE Transactions on Knowledge and Data Engineering
- 2021

Two practical distance sensitivity oracles for directed graphs as variants of Transit Node Routing are developed, one of which is made by applying the A* heuristics to the first oracle, which exploits lower bound distances to effectively reduce search space.

Revisiting path-type covering and partitioning problems.

- Mathematics
- 2018

Covering problems belong to the foundation of graph theory. There are several types of covering problems in graph theory such as covering the vertex set by stars (domination problem), covering the…

Utility-Aware Ridesharing on Road Networks

- Computer ScienceSIGMOD Conference
- 2017

Three efficient approximate algorithms are proposed, including a bilateral arrangement algorithm, an efficient greedy algorithm and a grouping-based scheduling algorithm, to assign riders to suitable vehicles with a high overall utility for utility-aware ridesharing on road networks.

Towards Scalable Subgraph Pattern Matching over Big Graphs on MapReduce

- Computer Science2016 IEEE 22nd International Conference on Parallel and Distributed Systems (ICPADS)
- 2016

This paper proposes a new approach, named ParMa, for efficient subgraph matching on distributed platforms, which consists of alternate computation and communication phases and introduces a suite of mechanisms, including join plan making, local join processing and join cost estimation, to join partial matches in an appropriate way to reduce its cost.

Fast exact shortest path and distance queries on road networks with parametrized costs

- Computer ScienceSIGSPATIAL/GIS
- 2015

With lightweight preprocessing the technique answers long-distance queries across continental networks significantly faster than previous approaches towards the same problem formulation.

C O ] 2 0 Ja n 20 21 The geodesic-transversal problem

- Mathematics
- 2021

A maximal geodesic in a graph is a geodesic (alias shortest path) which is not a subpath of a longer geodesic. The geodesic-transversal problem in a graph G is introduced as the task to find a…

Personalized route planning in road networks

- Computer ScienceSIGSPATIAL/GIS
- 2015

This work develops new preprocessing schemes that allow for real-time personalized route planning in huge road networks while keeping the memory footprint of the preprocessed data and subsequent queries small.

TS-Reconfiguration of k-Path Vertex Covers in Caterpillars

- Mathematics, Computer ScienceArXiv
- 2022

A polynomial-time algorithm is presented that solves k-PVCR under TS for caterpillars (i.e., trees formed by attaching leaves to a path), known to be PSPACE-complete even for planar graphs of maximum degree 3 and bounded treewidth.

A Fast and Tight Heuristic for A* in Road Networks

- Computer ScienceSEA
- 2021

An algorithm to efficiently extract distance estimates for A* from Contraction Hierarchies (CH), a hierarchical technique called CH-Potentials, which allows decoupling the supported extensions from the hierarchical speedup technique.

## References

SHOWING 1-10 OF 13 REFERENCES

On k-skip shortest paths

- Computer ScienceSIGMOD '11
- 2011

The proposed algorithms are the outcome of a careful theoretical analysis that reveals valuable insight into the characteristics of the k-skip <i>k</i>-skip SP computation in the context of spatial network databases (SNDB).

Polynomial-Time Construction of Contraction Hierarchies for Multi-Criteria Objectives

- Computer Science, MathematicsSOCS
- 2013

A variant of the multi-criteria shortest path problem where the different criteria are combined in an arbitrary conic combination at query time is considered, and it is proved via some polyhedral considerations that the crucial node contraction operation during the CH construction can be performed in polynomial time.

Exact Routing in Large Road Networks Using Contraction Hierarchies

- Computer ScienceTransp. Sci.
- 2012

A mobile implementation of contraction hierarchies for fast routing in road networks that also handles changes in the road network, like traffic jams, and that allows instantaneous routing without noticeable delay for the user is presented.

A Hub-Based Labeling Algorithm for Shortest Paths in Road Networks

- Computer ScienceSEA
- 2011

An implementation of the labeling algorithm that is faster than any existing method on continental road networks and has the best time bounds is described.

Customizable Route Planning

- Computer ScienceSEA
- 2011

We present an algorithm to compute shortest paths on continental road networks with arbitrary metrics (cost functions). The approach supports turn costs, enables real-time queries, and can…

Distance Preserving Graph Simplification

- Computer Science2011 IEEE 11th International Conference on Data Mining
- 2011

This paper constructs a gate graph from a large graph so that for any non-local vertex pair in the original graph, their shortest-path distance can be recovered by consecutive â€œlocalâ€ walks through the gate vertices in the gate graph.

VC-Dimension and Shortest Path Algorithms

- Computer ScienceICALP
- 2011

It is shown that set systems induced by sets of vertices on shortest paths have VC-dimension at most two, which allows a result from learning theory to improve time bounds on query algorithms for the point-to-point shortest path problem in networks of low highway dimension, such as road networks.

Fast routing in road networks using transit nodes

- Science, 316(5824):566
- 2007

Reach-Based Routing: A New Approach to Shortest Path Algorithms Optimized for Road Networks

- Computer ScienceALENEX/ANALC
- 2004