Scalable shortest paths browsing on land surface

Privacy preserving network publishing has been studied extensively in recent years. Although more works have adopted un-weighted graphs to model network relationships, weighted graph modeling can provide deeper analysis of the degree of relationships. Previous works on weighted graph privacy have concentrated on preserving the shortest path characteristic between pairs of vertices. Two common types of privacy have been proposed. One type of privacy tried to add random noise edge weights to the graph but still maintain the same shortest path. The other privacy, k-shortest path privacy, minimally perturbed edge weights so that there exists k shortest paths. However, the k-shortest path privacy only considers anonymizing same fixed number of shortest paths for all pairs of source and destination vertices. In this work, we present a new concept called [k1, k2]-shortest path privacy to allow different number of shortest paths for different pairs of vertices. A published network graph with [k1, k2]-shortest path privacy has at least k' indistinguishable shortest paths between the source and destination vertices, where k1 l k' l k2. A heuristic algorithm based on modifying only Non-Visited (NV) edges is proposed and experimental results showing the feasibility and characteristics of the proposed approach are presented.

We describe cellular-automaton-based algorithms for solving two shortest path problems on arbitrary connected, directed, and weighted graphs with n vertices. The first problem is that of finding the shortest path from a given vertex to another given vertex of the graph. A two-dimensional cellular automaton, shaped as a triangle, with \(O(n^2)\) cells, is used. The algorithm runs in O(n) time. The second problem requires that all shortest paths between pairs of vertices be obtained. An \(n \times n\) cellular automaton solves the problem in \(O(n \log n)\) time.

Point-to-point shortest path (PPSP), or s-t connectivity, is a variant of the shortest path problem found in graph theory. In this problem, we are given a graph and pairs of vertices over time, and the output is the shortest path between each pair of vertices. In this paper, we present two algorithms. Our first algorithm approximately solves the PPSP problem on any arbitrary graph. For each pair of vertices queried, it accurately and efficiently estimates the shortest path between the two vertices. Our second algorithm extends the first to work on dynamic graphs. That is, our second algorithm can efficiently account for changes in the graph, such as friend requests on the Facebook network or road closures on road networks. At a high level, both algorithms partition the graph into highly connected communities. To respond to a query q(u, v), they each find the fewest number of partitions between u and v, and the shortest path through each partition. We show that our static graph algorithm can approximate the distance between two vertices with about 20%-35% percent error and anywhere from 80X-70000X faster than a BFS in practice with the right choice of partitions. Additionally, we show that our dynamic graph algorithm can account for updates to the graph anywhere from 20X-20000X faster than rerunning the static graph algorithm for each change to the graph.

Network Intrusion Detection Systems (NIDSs) are an increasingly important tool for the prevention and mitigation of cyber attacks. Over the past years, a lot of research efforts have aimed at leveraging the increasingly powerful models of Machine Learning (ML) for this purpose. A number of labelled synthetic datasets have been generated and made publicly available by researchers, and they have become the benchmarks via which new ML-based NIDS classifiers are being evaluated. Recently published results show excellent classification performance with these datasets, increasingly approaching 100 percent performance across key evaluation metrics such as Accuracy, F1 score, AUC, etc. Unfortunately, we have not yet seen these excellent academic research results translated into practical NIDS systems with such near-perfect performance. This motivated our research presented in this paper, where we analyse the statistical properties of the benign traffic in three of the more recent and relevant NIDS datasets, (CIC_IDS, UNSW_NB15, TON_IOT), by converting them into a common flow format. As a comparison, we consider two datasets obtained from real-world production networks, one from a university network and one from a medium size Internet Service Provider (ISP). Our results show that the two real-world datasets are quite similar among themselves in regards to most of the considered statistical features. Equally, the three synthetic datasets are also relatively similar within their group. However, and most importantly, our results show a distinct difference of most of the considered statistical features between the three synthetic datasets and the two real-world datasets. Since ML relies on the basic assumption of training and test datasets being sampled from the same distribution, this raises the question of how well the performance results of ML-classifiers trained on the considered synthetic datasets can translate and generalise to real-world networks. We believe this is an interesting and relevant question which provides motivation for further research in this space.

We introduce a model for differentially private analysis of weighted graphs in which the graph topology (υ,e) is assumed to be public and the private information consists only of the edge weights ω : e → R+. This can express hiding congestion patterns in a known system of roads. Differential privacy requires that the output of an algorithm provides little advantage, measured by privacy parameters e and δ, for distinguishing between neighboring inputs, which are thought of as inputs that differ on the contribution of one individual. In our model, two weight functions w,w' are considered to be neighboring if they have l1 distance at most one.We study the problems of privately releasing a short path between a pair of vertices and of privately releasing approximate distances between all pairs of vertices. We are concerned with the approximation error, the difference between the length of the released path or released distance and the length of the shortest path or actual distance.For the problem of privately releasing a short path between a pair of vertices, we prove a lower bound of Ω(|υ|) on the additive approximation error for fixed privacy parameters e,δ. We provide a differentially private algorithm that matches this error bound up to a logarithmic factor and releases paths between all pairs of vertices, not just a single pair. The approximation error achieved by our algorithm can be bounded by the number of edges on the shortest path, so we achieve better accuracy than the worst-case bound for pairs of vertices that are connected by a low-weight path consisting of o(|υ|) vertices.For the problem of privately releasing all-pairs distances, we show that for trees we can release all-pairs distances with approximation error $O(log2.5|υ|) for fixed privacy parameters. For arbitrary bounded-weight graphs with edge weights in [0,M] we can brelease all distances with approximation error O(√>(|υ|M).

This article analyzes problems of determining the shortest path and optimal route amongst the given stoppages. The model of the problem is presented as a directional graph, where nodes are pickup points (termed as stoppage point in database) and crossings outside stoppage points and edges are roads among stoppage points and crossings. Each node has some information attached to it: stoppageId, stoppageName, latitude, longitude and numberOfPassengers of the stop, maintenance organizations, and mark(s) of the crossing(s). All pickup points are connected by roads. These roads are considered as the edges of the graph. Edges also have information attached to it: roadId, source, destination, distance, time etc.We have selected Floyd Warshall algorithm to nd the shortest path between two stoppages. This algorithm works in two stages: in rst stage, it nds the shortest path between all stoppages, and in second stage it nds optimized route to visit some of these stoppages. The solution is displayed in the form of shortest distance and time between two locations. The program is written in java language. It uses 3 tables as input from database : nodes, vehicle details and road. This paper gives implementation outcome of Floyd Warshall algorithm to solve the all pairs shortestpath problem for directed road graph system. We have considered an example of a map of Pune. Keyword: Adjacency matrix,intermediate path,optimal route, shortest path,transitive closure I. Introduction Now days in the current scenario companies and schools provide transportation facilities to their employees and students from their organizations to their respective houses and vice versa. The purpose of this article is to present an interface between a traveling agency and its traveller so that, the subscribers can keep a track of the service they have subscribed.A key problem in public conveyance system is the computation of shortest paths between di erent locations for a given region. Sometimes this computation has to be done in real time. During the literature survey we found how di cult it is to nd the shortest path covering all pickup points and how to allocate available transport vehicles to these speci c routes manually. There is always a need to nd optimal path for their operational viability. So, just the idea that our system will help in e cient allocation of vehicles and shortest route creation to save time and fuel consumption. The system scope is to design such system for a small area of the city.

We propose a simple and effective heuristic that allows fast generation of a large set of shortest path alternatives in weighted directed graphs. The heuristic is based on existing deviation path algorithms for exact k shortest paths. It precalculates a backward shortest path tree and thus avoids doing many shortest path computations, but as a result it does not necessarily find the exact set of k shortest paths. Computational results on real-world road networks are reported. Our tests show that the quality of the paths produced by the heuristic is most satisfactory: typically, the kth path found by the heuristic is less than 1% longer than the exact kth shortest path, for values of k up to 10,000. Moreover, the heuristic runs very fast. We also show how the heuristic can be enhanced to an exact k shortest paths algorithm, which performs well in comparison with the existing exact k shortest path algorithms.

Computing shortest paths in a directed graph has received considerable attention in the sequential RAM model of computation. However, developing a polylog-time parallel algorithm that is close to the sequential optimal in terms of the total work done remains an elusive goal. We present a first step in this direction by giving efficient parallel algorithms for shortest paths in planar layered digraphs. We show that these graphs admit special kinds of separators called {\em one-way} separators which allow the paths in the graph to cross it only once. We use these separators to give divide and conquer solutions to the problem of finding the shortest paths between any two vertices. We first give a simple algorithm that works in the CREW model and computes the shortest path between any two vertices in an $n$-node planar layered digraph in time $O(\log^3 n)$ using $n/ \log n$ processors. A CRCW version of this algorithm runs in time $O(\log^2 n \log \log n)$ and uses $n/ \log \log n$ processors. We then use results of Aggarwal and Park [1] and Atallah [4] to improve the time bound to $O(\log^2 n)$ in the CREW model and $O(\log n \log \log n)$ in the CRCW model. The processor bounds still remain as $n/ \log n$ for the CREW model and $n/ \log \log n$ for the CRCW model.

In various applications where the problem domain can be modeled into graphs, the shortest path computation in the graph is an indispensable challenge. In applications like online social networks and shortest route computation problems, the size of the graph is so large; the number of nodes have become close to hundreds of billions. Shortest path graph algorithms like SSSP (Single Source Shortest Path) and APSP (All Pairs Shortest Path) have low arithmetic intensity and irregular memory access patterns. The GPU implementation of many arithmetic and logical problems exceed the performance of the CPU system implementations. There is an increasing need for faster computation of shortest path in graphs for various applications. The objective of the work is to demonstrate that GPUs can efficiently perform shortest path computations on undirected weighted graphs considering space efficiency. For the implementation, GPUs supporting CUDA (Compute Unified Device Architecture) programming have been used. Additionally a space efficient approach called Triangular Matrix Method has been used.

In this paper we consider the decremental single-source shortest paths (SSSP) problem, where given a graph G and a source node s the goal is to maintain shortest paths between s and all other nodes in G under a sequence of online adversarial edge deletions. In their seminal work, Even and Shiloach [JACM 1981] presented an exact solution to the problem with only O(mn) total update time over all edge deletions. Their classic algorithm was the best known result for the decremental SSSP problem for three decades, even when approximate shortest paths are allowed. The first improvement over the Even-Shiloach algorithm was given by Bernstein and Roditty [SODA 2011], who for the case of an unweighted and undirected graph presented an approximate (1+) algorithm with constant query time and a total update time of O(n2+O(1/√logn)). This work triggered a series of new results, culminating in a recent breakthrough of Henzinger, Krinninger and Nanongkai [FOCS 14], who presented a -approximate algorithm whose total update time is near linear O(m1+ O(1/√logn)). In this paper they posed as a major open problem the question of derandomizing their result. In fact, all known improvements over the Even-Shiloach algorithm are randomized. All these algorithms maintain some truncated shortest path trees from a small subset of nodes. While in the randomized setting it is possible to “hide” these nodes from the adversary, in the deterministic setting this is impossible: the adversary can delete all edges touching these nodes, thus forcing the algorithm to choose a new set of nodes and incur a new computation of shortest paths. In this paper we present the first deterministic decremental SSSP algorithm that breaks the Even-Shiloach bound of O(mn) total update time, for unweighted and undirected graphs. Our algorithm is (1 + є) approximate and achieves a total update time of O(n2). Our algorithm can also achieve the same bounds in the incremental setting. It is worth mentioning that for dense instances where m = Ω(n2 − 1/√log(n)), our algorithm is also faster than all existing randomized algorithms.

Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.

Geographic Information Systems (GIS) are increasingly managing very large sets of data and hence a centralized data repository may not always provide the most scalable solution. Here we introduce a novel approach to manage spatial data by leveraging structured Peer-to-Peer (P2P) systems based on Distributed Hash Tables (DHTs). DHT algorithms provide efficient exact-match object search capabilities without requiring global indexing and as a result they are extremely scalable. Furthermore, the adoption of uniform hash functions ensures excellent load balancing. However, range queries -- which are very common with spatial data -- cannot be executed efficiently because the hash functions unfortunately destroy any existing data locality. Here we report on the design of an Adaptive Spatial Peer-to-pEer Network (ASPEN) that extends Content Addressable Networks (CAN) to preserve spatial locality information while also retaining many of the load balancing properties of DHT systems. We introduce the concept of scatter regions, which are spatial data distribution units that optimize both load balancing and spatial range query processing at the same time. We present a data object key generation function and algorithms for spatial range queries. We rigorously evaluate our technique with both synthetic and real world data sets and the results demonstrate the efficient execution of spatial range queries in the ASPEN system.

Problem statement: The processing of the XML queries needs an efficient indexing method. The index generation includes the labeling of the nodes. But for the dynamic data, when the changes are made, the re-computation of the labeling is needed. Approach: Based on the structural indexing used the performance of the query processing system will be affected. The dynamic XML document allows inserting, deleting and updating operations. Results: Suppose for the frequently changed documents, the indexes will also be changed. i.e., it requires the re-computing the labels frequently. This leads to an inconvenient system. To avoid this problem, in the scheme New Labeling Scheme for XML (NLSX), only the small, capital letters and digits are used to generate persistent labels for the nodes in the document. In the proposed system New Labeling Scheme for XML using Unicode Characters, characters from Unicode Characters (NLSXU) are used. Thus it can provide more combinations of the characters for persistent labeling the nodes in the document so that it will very much reduce the space needed to store the labels. Using the proposed scheme NLSXU, the index size of the real world data sets will be greatly reduced by 81% of the existing scheme NLSX. The results shows that the proposed scheme NLSXU will reduce the size of the indexes of the synthetic data sets up to 26, 34, 71 and 95% than the NLSX, LSDX, GRP and SP schemes respectively. Also when compared to LSDX scheme, the NLSXU will reduce the time taken for generating the labels by 96 and 80% for the real world datasets and the synthetic data sets respectively. Conclusion: Finally when compared to NLSX scheme, the NLSXU will reduce the time taken for generating the labels by 66 and 15% for the real world datasets and the synthetic data sets respectively. Thus it will improve the performance of the query system.

Shortest path computation using pulse-coupled neural networks with restricted autowave

In the civil aviation industry, the number of flights and the number of airports have been increasing. Airlines recommendation service which to provide customers with more efficient and shorter routes has become one of the effective measures for improving the service quality of aviation. Actually, Airports and air-lines can be formed a weighted directed graph (for example, we use plane fares to represent the weights on the edges of the graph, and represent the vertices in the graph by the airports), and Airlines recommendation is to help user to find out the shortest path from the source vertex to the target vertices of the weighted directed graph. The shortest path search can be done by using the Dijkstra incremental optimization algorithm[1]. However, as the incremental part become larger and larger, the time spent on shortest path computation will be growing rapidly. In order to shorten the computing time, this paper proposes a dynamic SPT increment algorithm based on Hadoop platform. By the Hadoop efficient distributed platform[2], using MapReduce to take a dynamic search for the incremental part of the SPT. Finally, regenerates the new shortest path tree to improve the algorithm efficiency and performance.