The field of graph algorithms and data structures is moving towards developing more efficient and scalable solutions for complex problems. Researchers are focusing on designing novel algorithms and data structures that can handle large-scale graphs and provide near-optimal solutions. One of the key directions is the development of approximation algorithms for various graph problems, such as the Traveling Salesman Problem and the Steiner Tree Problem. Another area of interest is the design of efficient data structures for graph analysis, such as distance oracles and spanners. Additionally, there is a growing interest in studying the computational complexity of graph problems and developing parameterized algorithms to solve them. Noteworthy papers in this area include a new approximation algorithm for the Graphic Multi-Path TSP with a significantly improved approximation guarantee, and a comprehensive study of distance oracles with non-constant query time, which presents a new three-way trade-off between stretch, space, and query time.
Advances in Graph Algorithms and Data Structures
Sources
Distance-based (and path-based) covering problems for graphs of given cyclomatic number
Approximating Graphic Multi-Path TSP and Graphic Ordered TSP
New approximate distance oracles and their applications
Hitting Geodesic Intervals in Structurally Restricted Graphs
The Price of Connectivity Augmentation on Planar Graphs
Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
Arcs with increasing chords in $\mathbf{R}^d$
Fast approximation algorithms for the 1-median problem on real-world large graphs
Additive, Near-Additive, and Multiplicative Approximations for APSP in Weighted Undirected Graphs: Trade-offs and Algorithms
Efficient Exact Resistance Distance Computation on Small-Treewidth Graphs: a Labelling Approach
Algorithmic Information Bounds for Distances and Orthogonal Projections
Well-Separated Pairs Decomposition Revisited
The Steiner Shortest Path Tree Problem
How to Reconfigure Your Alliances