Related papers: Weighted graph algorithms with Python
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Finding shortest paths in a given network (e.g., a computer network or a road network) is a well-studied task with many applications. We consider this task under the presence of an adversary, who can manipulate the network by perturbing its…
For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are…
Many exact search algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as vertex/edge…
In this paper I present general outlook on questions relevant to the basic graph algorithms; Finding the Shortest Path with Positive Weights and Minimum Spanning Tree. I will show so far known solution set of basic graph problems and…
The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…
Consider the following 2-respecting min-cut problem. Given a weighted graph $G$ and its spanning tree $T$, find the minimum cut among the cuts that contain at most two edges in $T$. This problem is an important subroutine in Karger's…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…
The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…
We propose a novel algorithm for enumerating and listing all minimal cutsets of a given graph. It is known that this problem is NP-hard. We use connectivity properties of a given graph to develop an algorithm with reduced complexity for…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…
Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
The minimum cost multicut problem is the NP-hard/APX-hard combinatorial optimization problem of partitioning a real-valued edge-weighted graph such as to minimize the total cost of the partition. While graph convolutional neural networks…
Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…
We consider the problem of finding edges of a hidden weighted graph using a certain type of queries. Let $G$ be a weighted graph with $n$ vertices. In the most general setting, the $n$ vertices are known and no other information about $G$…
We study a constrained shortest path problem in group-labeled graphs with nonnegative edge length, called the shortest non-zero path problem. Depending on the group in question, this problem includes two types of tractable variants in…
We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case…