In the PLANAR DISJOINT PATHS problem, one is given an undirected planar graph with a
set of k vertex pairs \left(s_i,t_i\right) and the task is to find k pairwise vertex-disjoint paths …

The disjoint paths problem is a fundamental problem in algorithmic graph theory and
combinatorial optimization. For a given graph G and a set of k pairs of terminals in G, it asks …

Urban traffic congestion is a pressing issue, demanding effective and cost-efficient solutions.
This paper develops the Traffic Weighted Multi-Maps (TWM) method to solve the Traffic …

Traffic engineering (TE) is a fundamental task in networking. Conventionally, traffic can take
any path connecting the source and destination. Emerging technologies such as segment …

We study the algorithmic complexity of partitioning the vertex set of a given (di) graph into a
small number of paths. The Path Partition problem (PP) has been studied extensively, as it …

Given an undirected-vertex graph and pairs of terminal vertices, the-Disjoint Shortest Paths (-
SDP) problem asks whether there are pairwise vertex-disjoint paths such that is a shortest …

With the emergence of IoT applications, 5G, and edge computing, network resource
allocation has shifted toward the edge, bringing services closer to the end users. These …

The k disjoint shortest paths problem (k-DSPP) on a graph with k source–sink pairs (si, ti)
asks if there exist k pairwise edge-or vertex-disjoint shortest si–t i-paths. It is known to be NP …

In the $ k $-Disjoint Shortest Paths ($ k $-DSP) problem, we are given a weighted graph $ G
$ on $ n $ nodes and $ m $ edges with specified source vertices $ s_1,\dots, s_k $, and …

This note summarizes the state of what is known about the tractability of the problem
ModPath, which asks if an input undirected graph contains a simple st-path whose length …