Single Source Shortest Path Algorithm Research Articles

Priority queues with decreasing keys

A priority queue stores a multiset of items, each item being a 〈key,value〉 pair, and supports the insertion of a new item and extraction of an item with minimum key. In applications like Dijkstra's single source shortest path algorithm and Prim-Jarník's minimum spanning tree algorithm, the key of an item can decrease over time. Usually this is handled by either using a priority queue supporting the deletion of an arbitrary item or a dedicated DecreaseKey operation, or by inserting the same item multiple times but with decreasing keys.In this paper we study what happens if the keys associated with the items in a priority queue can decrease over time without informing the priority queue, and how such a priority queue can be used in Dijkstra's algorithm. We show that binary heaps with bottom-up insertions fail to report items with unchanged keys in correct order, while binary heaps with top-down insertions report items with unchanged keys in correct order. Furthermore, we show that skew heaps, leftist heaps, and priority queues based on linking the roots of heap-ordered trees, like pairing heaps, binomial queues and Fibonacci heaps, work correctly with decreasing keys without any modifications. Finally, we show that the post-order heap by Harvey and Zatloukal, a variant of a binary heap with amortized constant time insertions and amortized logarithmic time deletions, works correctly with decreasing keys and is a strong contender for an implicit priority queue supporting decreasing keys in practice.

An efficient SSSP algorithm on time-evolving graphs with prediction of computation results

Many applications need to execute Single-Source Shortest Paths (SSSP) algorithm on each snapshot of a time-evolving graph, leading to long waiting times experienced by the users of such applications. However, these applications are often time-sensitive, the delayed computation results can lead to the loss of best decision-making opportunities. To address this problem, in this paper we propose an efficient SSSP algorithm for time-evolving graphs, called V-Grouper. The main idea of V-Grouper is to avoid the redundant computations of the same vertex in different snapshots. Our experimental results over real-world time-evolving graphs show that, due to the high similarity of consecutive snapshots, the computation results of one vertex in neighboring snapshots are equal with a high probability. At the beginning of computation, V-Grouper first divides all the versions of a given vertex in different snapshots into vertex groups, where the computation result of each version is predicted based on the aforementioned insight of neighboring snapshots having equal results. The versions of the vertex in each group have the same predicted computation result. During the computation process for each vertex group, only one version needs to participate in computation, avoiding a large number of redundant computations. Experimental results show that V-Grouper is up to 64.31× faster than the state-of-the-art SSSP algorithm.

Graph based routing algorithm for torus topology and its evaluation for the Angara interconnect

Several approaches and techniques exist to resolve load balancing problem in general and torus topology networks. Graph methods are natural ways to perform balancing of routing paths. A routing balancing algorithm must operate within the constraints of the underlying network architecture that limits several parameters, such as the number of logical paths in the network. In this paper, we consider a torus topology that is one of the common topologies that are used in high performance computing systems. We introduce a routing graph that corresponds to a interconnect topology, abstracts interconnect routing rules, providing one-to-one correspondence of network routes and graph paths. We propose a deadlock-free routing algorithm based on a fast single-source shortest path algorithm in a routing graph for the deterministic routing of a torus topology interconnect with a single virtual channel. The proposed algorithm is a tradeoff between two existing routing algorithms, also the algorithm is optimized for multidimensional torus topology and can be applied to any torus topology HPC system. We present a complete description of a routing graph that abstracts the Angara interconnect with 4D torus topology. We evaluated the proposed routing algorithm and benchmarked the maximum performance improvement of 71% for the Alltoall pattern for torus topology systems up to 432 nodes on the Angara interconnect simulator. The performance improvement of more than 5% was obtained for the NPB FT and IS application kernels on a 32-node supercomputer.

A fast phenotype approach of 3D point clouds of Pinus massoniana seedlings.

The phenotyping of Pinus massoniana seedlings is essential for breeding, vegetation protection, resource investigation, and so on. Few reports regarding estimating phenotypic parameters accurately in the seeding stage of Pinus massoniana plants using 3D point clouds exist. In this study, seedlings with heights of approximately 15-30 cm were taken as the research object, and an improved approach was proposed to automatically calculate five key parameters. The key procedure of our proposed method includes point cloud preprocessing, stem and leaf segmentation, and morphological trait extraction steps. In the skeletonization step, the cloud points were sliced in vertical and horizontal directions, gray value clustering was performed, the centroid of the slice was regarded as the skeleton point, and the alternative skeleton point of the main stem was determined by the DAG single source shortest path algorithm. Then, the skeleton points of the canopy in the alternative skeleton point were removed, and the skeleton point of the main stem was obtained. Last, the main stem skeleton point after linear interpolation was restored, while stem and leaf segmentation was achieved. Because of the leaf morphological characteristics of Pinus massoniana, its leaves are large and dense. Even using a high-precision industrial digital readout, it is impossible to obtain a 3D model of Pinus massoniana leaves. In this study, an improved algorithm based on density and projection is proposed to estimate the relevant parameters of Pinus massoniana leaves. Finally, five important phenotypic parameters, namely plant height, stem diameter, main stem length, regional leaf length, and total leaf number, are obtained from the skeleton and the point cloud after separation and reconstruction. The experimental results showed that there was a high correlation between the actual value from manual measurement and the predicted value from the algorithm output. The accuracies of the main stem diameter, main stem length, and leaf length were 93.5%, 95.7%, and 83.8%, respectively, which meet the requirements of real applications.

An algorithmic framework for the single source shortest path problem with applications to disk graphs

Shortest path problems are among the fundamental problems in graph theory. It is folklore that the unweighted single source shortest path (SSSP) problem in general graphs can be solved optimally with breadth first search (BFS) in O(n+m) time. In this paper, we develop an algorithmic framework that generalizes a batched BFS approach to give efficient SSSP algorithms for several graph classes. The running time of these algorithms depends on the running time of three main ingredients. The first is a preprocessing step, to define a shortcut graph that maintains some distance information. Then during one run of the algorithm repeatably there are the steps of efficiently finding a set of candidate vertices adjacent in the shortcut graph to a given set of vertices and finally finding the subset of the candidate vertices that actually form an edge in the original graph.A disk graphD(S) is a graph that is defined on a set S of point sites in R2, where each site s∈S has an associated radius rs. The vertex set of D(S) is S and two sites s,t are connected by an edge st in D(S) if and only if the disks induced by s and t intersect. These graphs are also called the intersection graph of disks. Our results are algorithms that use the framework to efficiently solve the SSSP problem in intersection graphs. For disk graphs in the L2-metric, we can show that after O(nlog2⁡n) preprocessing time we can solve the SSSP problem in O(nlog⁡n) time. This significantly improves the previous best bound of O(nlog4⁡n)[1,2]. In the case of intersection graphs of axis-parallel squares, we are even able to reduce the preprocessing time to an optimal O(nlog⁡n). As intersection graphs of axis parallel squares are equivalent to disk graphs in the L1- and L∞-metric the result carries over to these metrics.To show further applications of our framework, we restate the classical BFS, and also the optimal SSSP algorithm for unit disk graphs by Chan and Skrepetos [3] in our framework, showing its robustness.

A Parallel Algorithm Template for Updating Single-Source Shortest Paths in Large-Scale Dynamic Networks

The Single Source Shortest Path (SSSP) problem is a classic graph theory problem that arises frequently in various practical scenarios; hence, many parallel algorithms have been developed to solve it. However, these algorithms operate on static graphs, whereas many real-world problems are best modeled as dynamic networks, where the structure of the network changes with time. This gap between the dynamic graph modeling and the assumed static graph model in the conventional SSSP algorithms motivates this work. We present a novel parallel algorithmic framework for updating the SSSP in large-scale dynamic networks and implement it on the shared-memory and GPU platforms. The basic idea is to identify the portion of the network affected by the changes and update the information in a rooted tree data structure that stores the edges of the network that are most relevant to the analysis. Extensive experimental evaluations on real-world and synthetic networks demonstrate that our proposed parallel updating algorithm is scalable and, in most cases, requires significantly less execution time than the state-of-the-art recomputing-from-scratch algorithms.

Accelerating SSSP for Power-Law Graphs.

The single-source shortest path (SSSP) problem is one of the most important and well-studied graph problems widely used in many application domains, such as road navigation, neural image reconstruction, and social network analysis. Although we have known various SSSP algorithms for decades, implementing one for large-scale power-law graphs efficiently is still highly challenging today, because ① a work-efficient SSSP algorithm requires priority-order traversal of graph data, ② the priority queue needs to be scalable both in throughput and capacity, and ③ priority-order traversal requires extensive random memory accesses on graph data. In this paper, we present SPLAG to accelerate SSSP for power-law graphs on FPGAs. SPLAG uses a coarse-grained priority queue (CGPQ) to enable high-throughput priority-order graph traversal with a large frontier. To mitigate the high-volume random accesses, SPLAG employs a customized vertex cache (CVC) to reduce off-chip memory access and improve the throughput to read and update vertex data. Experimental results on various synthetic and real-world datasets show up to a 4.9× speedup over state-of-the-art SSSP accelerators, a 2.6× speedup over 32-thread CPU running at 4.4 GHz, and a 0.9× speedup over an A100 GPU that has 4.1× power budget and 3.4× HBM bandwidth. Such a high performance would place SPLAG in the 14th position of the Graph 500 benchmark for data intensive applications (the highest using a single FPGA) with only a 45 W power budget. SPLAG is written in high-level synthesis C++ and is fully parameterized, which means it can be easily ported to various different FPGAs with different configurations. SPLAG is open-source at https://github.com/UCLA-VAST/splag.

Uncovering input-sensitive energy bottlenecks in oversubscribed GPU workloads

Graph algorithms are at the core of data-intensive applications in many computational domains. Although accelerator-based implementations have the potential for delivering improved energy efficiency on today’s large-scale graph analytics, there are many challenges to reaching the desired goals. This paper examines the issues of GPU oversubscription and input sensitivity in energy efficient graph processing. We introduce the notion of energy signatures, a collection of runtime events that can determine fluctuations in power consumption as a function of input graph characteristics. The study shows that variations in volume, density, diameter and dispersion in graphs can alter the runtime behavior of GPU applications and these changes in program behavior in turn impact the energy efficiency of the application. Based on the insight gained from our study, we develop three input-aware optimization techniques to mitigate energy bottlenecks. On experiments conducted on a Unified Memory supported GPU, the optimizations yield a 11.97% energy savings on average on Breadth-First Search and Single-Source Shortest Path algorithms.

DP-solver: automating dynamic programming

Abstract Dynamic programming (DP) is a widely used optimization method with several applications in various fields of science. The DP problem solving process can be divided in two phases: mathematical part and programming part. There are a number of researchers for whom the mathematical part is available, but they are not familiar with computer programming. In this paper we present a software tool that automates the programming part of DP and allows users to solve problems based only on their mathematical approach. The application builds up the “d-graph model” of the problem to be solved and applies the “d-variant” of the corresponding single source shortest path algorithm. In addition, we report experimental results regarding the e ciency of the tool relative to the Matlab implementation.

Parallel Algorithm on GPU for Wireless Sensor Data Acquisition Using a Team of Unmanned Aerial Vehicles.

This paper proposes a framework for the wireless sensor data acquisition using a team of Unmanned Aerial Vehicles (UAVs). Scattered over a terrain, the sensors detect information about their surroundings and can transmit this information wirelessly over a short range. With no access to a terrestrial or satellite communication network to relay the information to, UAVs are used to visit the sensors and collect the data. The proposed framework uses an iterative k-means algorithm to group the sensors into clusters and to identify Download Points (DPs) where the UAVs hover to download the data. A Single-Source–Shortest-Path algorithm (SSSP) is used to compute optimal paths between every pair of DPs with a constraint to reduce the number of turns. A genetic algorithm supplemented with a 2-opt local search heuristic is used to solve the multi-travelling salesperson problem and to find optimized tours for each UAVs. Finally, a collision avoidance strategy is implemented to guarantee collision-free trajectories. Concerned with the overall runtime of the framework, the SSSP algorithm is implemented in parallel on a graphics processing unit. The proposed framework is tested in simulation using three UAVs and realistic 3D maps with up to 100 sensors and runs in just 20.7 s, a 33.3× speed-up compared to a sequential execution on CPU. The results show that the proposed method is efficient at calculating optimized trajectories for the UAVs for data acquisition from wireless sensors. The results also show the significant advantage of the parallel implementation on GPU.

Single-source shortest paths and strong connectivity in dynamic planar graphs

We give a fully dynamic single-source shortest paths data structure for planar weighted digraphs with O˜(n4/5) worst-case update time and O(log2⁡n) query time. Here, a single update can either change the graph by inserting or deleting an edge, or reset the source s of interest. All known non-trivial planarity-exploiting exact dynamic single-source shortest paths algorithms to date had polynomial query time. We then extend our approach, obtaining a data structure that can maintain a planar digraph under edge insertions and deletions, and is capable of returning the identifier of the strongly connected component of any query vertex. The worst-case update and query time bounds are the same as for our single-source distance oracle. To the best of our knowledge, this is the first fully dynamic strong-connectivity algorithm achieving both sublinear update time and polylogarithmic query time for an important class of digraphs.

RETRACTED ARTICLE: Implementation of MapReduce parallel computing framework based on multi-data fusion sensors and GPU cluster

Nowadays, with the rapid growth of data volume, massive data has become one of the factors that plague the development of enterprises. How to effectively process data and reduce the concurrency pressure of data access has become the driving force for the continuous development of big data solutions. This article mainly studies the MapReduce parallel computing framework based on multiple data fusion sensors and GPU clusters. This experimental environment uses a Hadoop fully distributed cluster environment, and the entire programming of the single-source shortest path algorithm based on MapReduce is implemented in Java language. 8 ordinary physical machines are used to build a fully distributed cluster, and the configuration environment of each node is basically the same. The MapReduce framework divides the request job into several mapping tasks and assigns them to different computing nodes. After the mapping process, a certain intermediate file that is consistent with the final file format is generated. At this time, the system will generate several reduction tasks and distribute these files to different cluster nodes for execution. This experiment will verify the changes in the running time of the PSON algorithm when the size of the test data set gradually increases while keeping the hardware level and software configuration of the Hadoop platform unchanged. When the number of computing nodes increases from 2 to 4, the running time is significantly reduced. When the number of computing nodes continues to increase, the reduction in running time will become less and less significant. The results show that NESTOR can complete the basic workflow of MapReduce, and simplifies the process of user development of GPU positive tree order, which has a significant speedup for applications with large amounts of calculations.

Position Paper: Dijkstra's Algorithm versus Uniform Cost Search or a Case Against Dijkstra's Algorithm

Dijkstra's single-source shortest-path algorithm (DA) is one of the well-known, fundamental algorithms in computer science and related fields. DA is commonly taught in undergraduate courses. Uniform-cost search (UCS) is a simple version of the best-first search scheme which is logically equivalent to DA. In this paper I compare the two algorithms and show their similarities and differences. I claim that UCS is superior to DA in almost all aspects. It is easier to understand and implement. Its time and memory needs are also smaller. The reason that DA is taught in universities and classes around the world is probably only historical. I encourage people to stop using and teaching DA, and focus on UCS only.

A distributed algorithm for directed minimum-weight spanning tree

In the directed minimum spanning tree problem (DMST, also called minimum weight arborescence), we are given a directed weighted graph, and a root node r. Our goal is to construct a minimum-weight directed spanning tree, rooted at r and oriented outwards. We present the first sub-quadratic DMST algorithm in the distributed \({\mathsf {CONGEST}}\) network model, where the messages exchanged between the network nodes are bounded in size. We consider three versions of the model: a network where the communication links are bidirectional but can have different weights in the two directions; a network where communication is unidirectional; and the Congested Clique model, where all nodes can communicate directly with each other. Our DMST algorithm is based on a variant of Lovász’ DMST algorithm for the PRAM model, and uses a distributed single-source shortest-path (SSSP) algorithm for directed graphs as a black box. In the bidirectional \({\mathsf {CONGEST}}\) model, our algorithm has roughly the same running time as the SSSP algorithm that is used as a black box; using the state-of-the-art SSSP algorithm due to Chechik and Mukhtar (in: Symposium on principles of distributed computing (PODC), ACM, 2020, pp 464–473), we obtain a running time of \({\widetilde{O}}(\sqrt{n}D^{1/4}+D))\) rounds for the bidirectional communication case. For the unidirectional communication model we give an \({\widetilde{O}}(n)\) algorithm, and show that it is nearly optimal. And finally, for the Congested Clique, our algorithm again matches the best known SSSP algorithm: it runs in \({\widetilde{O}}(n^{1/3})\) rounds. On the negative side, we adapt an observation of Chechik in the sequential setting to show that in all three models, the DMST problem is at least as hard as the (s, t)-shortest path problem. Thus, in terms of round complexity, distributed DMST lies between single-source shortest path and (s, t)-shortest path.

Development Trend of Intelligent Transportation in the Era of Big Data

The arrival of the big data era has brought great convenience to people’s real life. All aspects of our lives follow the development of the big data era. In the context of the era of big data, through data collection and analysis, the current urban transportation has been reasonably developed, laying a good foundation for the development of intelligent transportation in the future, and can solve various current problems. Based on the analysis of the traffic system, this article finds that the real-time road condition prediction of common functions is highly correlated with route guidance. Therefore, this paper uses a method based on historical data to predict road conditions, and uses the prediction results to dynamically allocate road segments, and then uses the relevant single-source shortest path algorithm to simulate the optimal path. By analyzing the application advantages of data mining in intelligent transportation, Baum Welch’s algorithm is used for data mining in a real-time traffic prediction system based on historical data. Real-time road conditions are matched with historical data models to predict road conditions. Finally, analyzed and designed the big data cloud platform framework applied to it to achieve higher efficiency. The experimental research results show that, by studying the development of urban intelligent transportation systems, the purpose of this paper is to make better use of existing resources to process data more efficiently, and then combine distributed data mining algorithms to optimize the processed data and apply it to in the intelligent transportation system, an intelligent management and control system that is more efficient, accurate, and user experience better can be established.

Hoshin Kanri’s Strategic Planning Methodology through Dijkstra Algorithm within Industrial Engineering and Stakeholder Perspectives

Hoshin Kanri is defined as strategic planning methodology to reinforce strategic work. This paper elaborates Hoshin Kanri’s strategic planning methodology through Dijkstra algorithm within industrial Engineering and stakeholder perspectives. Dijkstra’s algorithm is categorized as the single source shortest path algorithm. This algorithm is beneficial to measure the shortest distance on a directed and undirected path within delivery optimization. This paper objective is to evaluate strategic planning in term of delivery optimization and scheduling. Subsequently, by implementing the strategic planning, it is expected to improve existing distribution process in supply chain. Other than that, it is expected to reduce and optimize delivery’s cost within its scheduling process through lens of industrial engineering and stakeholder priority. The research methodology in this paper refers to the quantitative approaches. These approaches are within sales performance’s data collection in modern market and its customer address. Furthermore, the data analysis proceeds to purchasing power of each customer. Ultimately, the mentioned analysis scheduling method through routing planning is using Dijkstra’s Algorithm. The mentioned Dijkstra Algorithm’s delivery optimization and scheduling is through lens of industrial engineering and Stakeholder. The result and discussion of this paper elaborates analysis and its decision making toward strategic planning in order to accommodate stakeholder perspectives.

SRide: An Online System for Multi-Hop Ridesharing

In the context of smart cities, ridesharing in urban areas is gaining researchers’ interest and is considered to be a sustainable transportation solution. In this paper, we present SRide (Shared Ride), a multi-hop ridesharing system as a mode of sustainable transportation. Multi-hop ridesharing is a type of ridesharing in which a rider travels in multiple hops to reach a destination, transferring from one driver to another between hops. The key problem in multi-hop ridesharing is to find an optimal itinerary or route plan for a rider from an origin to a destination in a dynamic, online setting. SRide adopts a novel approach to finding itineraries for riders suited to the online nature of the problem. The system represents ride offers as a time-dependent directed graph and finds itineraries dynamically by updating the graph incrementally and decrementally as ride offers are updated in the system. The system’s distinguishing feature is its incremental and decremental operation, which is enabled by employing dynamic single-source shortest-path algorithms. We conducted two extensive simulation studies to evaluate its performance. Metrics, including the matching rate, savings in total system-wide vehicle-miles, and total system-wide driving times were measured. In the first study, SRide’s dynamic update algorithms were compared with their non-dynamic versions. Results show that SRide’s algorithms run up to thirteen times faster than their non-dynamic versions. In the second study, we used data from the travel demand model for metropolitan Atlanta in the US state of Georgia, to assess the benefits of multi-hop ridesharing. Results show that matching rates increase up to 68%, saving in total system-wide vehicle-miles of up to 12%, and reduction in the total system-wide driving time of up to 12.86% is achieved.

Optimal Fuel Saving in 4D Waypoint Networks

The purpose of this work is to develop a trajectory optimization method that generates a fuel optimal trajectory from a predefined 4D waypoint networks, where the arrival time is specified for each waypoint in the network. A single source shortest path algorithm is presented to generate the optimal flight trajectory that minimizes fuel burn. Generating such trajectories enables the airlines to cope with increasing fuel costs and to reduce aviation induced climate change, as emission is directly related to the amount of fuel burn. Two case studies were considered and the simulation results showed that flying a fuel optimal trajectory based on the proposed algorithm leads to a reduction of average fuel consumption on international flights by 2-4% compared with the conventional trip fuel.
 Keywords: Fuel saving, Cost index, 4D trajectory optimization, Waypoint network, Dijkstra’s algorithm

Fast approximate shortest paths in the congested clique

We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include:A (2+epsilon )-approximation for all-pairs shortest paths in O(log ^2{n} / epsilon ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model.A (1+epsilon )-approximation for multi-source shortest paths from O(sqrt{n}) sources in O(log ^2{n} / epsilon ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in tilde{O}(n^{1/6}) rounds.

A single-source shortest path algorithm for dynamic graphs

Graphs are mathematical structures used in many applications. In recent years, many applications emerged that require the processing of large dynamic graphs where the graph’s structure and properties change constantly over time. Examples include social networks, communication networks, transportation networks, etc. One of the most challenging problems in large scale dynamic graphs is the single-source shortest path (SSSP) problem. Traditional solutions (based on Dijkstra’s algorithms) to the SSSP problem do not scale to large dynamic graphs with a high change frequency. In this paper, we propose an efficient SSSP algorithm for large dynamic graphs. We first present our algorithm and give a formal proof of its correctness. Then, we give an analytical evaluation of the proposed solution.