Related papers: On The Optimization of Dijkstras Algorithm
{\em Reoptimization} is a setting in which we are given an (near) optimal solution of a problem instance and a local modification that slightly changes the instance. The main goal is that of finding an (near) optimal solution of the…
Dijkstra's algorithm for the Single-Source Shortest Path (SSSP) problem is notoriously hard to parallelize in $o(n)$ depth, $n$ being the number of vertices in the input graph, without increasing the required parallel work unreasonably.…
This paper formulates a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. The smoothness condition…
Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is…
We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes…
Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of…
Motivated by efforts to incorporate sheaves into networking, we seek to reinterpret pathfinding algorithms in terms of cellular sheaves, using Dijkstra's algorithm as an example. We construct sheaves on a graph with distinguished source and…
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy.…
We give an algorithm that decides whether the bipartite crossing number of a given graph is at most $k$. The running time of the algorithm is upper bounded by $2^{O(k)} + n^{O(1)}$, where $n$ is the number of vertices of the input graph,…
When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. To amend the limitation, numbers of improved schemes are proposed. In this paper,…
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…
Let G be a weighted (directed) graph with n vertices and m edges. Given a source vertex s, Dijkstra's algorithm computes the shortest path lengths from s to all other vertices in O(m + n log n) time. This bound is known to be worst-case…
In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or…
In this paper we prove that Dijkstra's shortest-path algorithm, if implemented with a sufficiently efficient heap, is universally optimal in its running time, and with suitable small additions is also universally optimal in its number of…
We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent…
The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
Bilevel optimization has been widely applied in many important machine learning applications such as hyperparameter optimization and meta-learning. Recently, several momentum-based algorithms have been proposed to solve bilevel optimization…