• Title/Summary/Keyword: K shortest paths problem

Search Result 36, Processing Time 0.024 seconds

A Border Line-Based Pruning Scheme for Shortest Path Computations

  • Park, Jin-Kyu;Moon, Dae-Jin;Hwang, Een-Jun
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.4 no.5
    • /
    • pp.939-955
    • /
    • 2010
  • With the progress of IT and mobile positioning technologies, various types of location-based services (LBS) have been proposed and implemented. Finding a shortest path between two nodes is one of the most fundamental tasks in many LBS related applications. So far, there have been many research efforts on the shortest path finding problem. For instance, $A^*$ algorithm estimates neighboring nodes using a heuristic function and selects minimum cost node as the closest one to the destination. Pruning method, which is known to outperform the A* algorithm, improves its routing performance by avoiding unnecessary exploration in the search space. For pruning, shortest paths for all node pairs in a map need to be pre-computed, from which a shortest path container is generated for each edge. The container for an edge consists of all the destination nodes whose shortest path passes through the edge and possibly some unnecessary nodes. These containers are used during routing to prune unnecessary node visits. However, this method shows poor performance as the number of unnecessary nodes included in the container increases. In this paper, we focus on this problem and propose a new border line-based pruning scheme for path routing which can reduce the number of unnecessary node visits significantly. Through extensive experiments on randomly-generated, various complexity of maps, we empirically find out optimal number of border lines for clipping containers and compare its performance with other methods.

Essential Arcs of a Directed Acyclic Graph

  • Chung, Ee-Suk
    • Management Science and Financial Engineering
    • /
    • v.13 no.1
    • /
    • pp.121-126
    • /
    • 2007
  • Among many graphs, directed acyclic graph(DAG) attracts many researchers due to its nice property of existence of topological sort. In some classic graph problems, it is known that, if we use the aforementioned property, then much efficient algorithms can be generated. So, in this paper, new algorithm for the all-pairs shortest path problem in a DAG is proposed. While the algorithm performing the iteration, it identifies the set of essential arcs which requires in a shortest path. So, the proposed algorithm has a running time of $O(m^*n+m)$, where m, n and $m^*$ denote the number of arcs, number of node, and the number of essential arcs in a DAG, respectively.

Multiple Path Based Vehicle Routing in Dynamic and Stochastic Transportation Networks

  • Park, Dong-joo
    • Proceedings of the KOR-KST Conference
    • /
    • 2000.02a
    • /
    • pp.25-47
    • /
    • 2000
  • In route guidance systems fastest-path routing has typically been adopted because of its simplicity. However, empirical studies on route choice behavior have shown that drivers use numerous criteria in choosing a route. The objective of this study is to develop computationally efficient algorithms for identifying a manageable subset of the nondominated (i.e. Pareto optimal) paths for real-time vehicle routing which reflect the drivers' preferences and route choice behaviors. We propose two pruning algorithms that reduce the search area based on a context-dependent linear utility function and thus reduce the computation time. The basic notion of the proposed approach is that ⅰ) enumerating all nondominated paths is computationally too expensive, ⅱ) obtaining a stable mathematical representation of the drivers' utility function is theoretically difficult and impractical, and ⅲ) obtaining optimal path given a nonlinear utility function is a NP-hard problem. Consequently, a heuristic two-stage strategy which identifies multiple routes and then select the near-optimal path may be effective and practical. As the first stage, we utilize the relaxation based pruning technique based on an entropy model to recognize and discard most of the nondominated paths that do not reflect the drivers' preference and/or the context-dependency of the preference. In addition, to make sure that paths identified are dissimilar in terms of links used, the number of shared links between routes is limited. We test the proposed algorithms in a large real-life traffic network and show that the algorithms reduce CPU time significantly compared with conventional multi-criteria shortest path algorithms while the attributes of the routes identified reflect drivers' preferences and generic route choice behaviors well.

  • PDF

Using Evolution Program to Develop Effective Search Method for Alternative Routes (진화 프로그램을 이용한 효율적인 대체경로 탐색방법 연구)

  • CHOI, Gyoo Seok;SEO, Ki Sung;PARK, Jong Jin
    • Journal of Korean Society of Transportation
    • /
    • v.20 no.2
    • /
    • pp.71-79
    • /
    • 2002
  • This paper presents an effective alternative K-paths calculation method based on a Evolution Program (EP). We developed efficient genetic operators for path calculation. A major problem of the existing approach(similarities among the paths) can be resolved using EP's. The performance of the suggested method is evaluated and compared with the k-th shortest path for the virtual road network model by computer simulation. The results of computational experiments of the suggested method are found to be satisfactory in terms of the dispersion of alternatives.

QoS-Aware Approach for Maximizing Rerouting Traffic in IP Networks

  • Cui, Wenyan;Meng, Xiangru;Yang, Huanhuan;Kang, Qiaoyan;Zhao, Zhiyuan
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.10 no.9
    • /
    • pp.4287-4306
    • /
    • 2016
  • Network resilience provides an effective way to overcome the problem of network failure and is crucial to Internet protocol (IP) network management. As one of the main challenges in network resilience, recovering from link failure is important to maintain the constancy of packets being transmitted. However, existing failure recovery approaches do not handle the traffic engineering problem (e.g., tuning the routing-protocol parameters to optimize the rerouting traffic flow), which may cause serious congestions. Moreover, as the lack of QoS (quality of service) restrictions may lead to invalid rerouting traffic, the QoS requirements (e.g., bandwidth and delay) should also be taken into account when recovering the failed links. In this paper, we first develop a probabilistically correlated failure model that can accurately reflect the correlation between link failures, with which we can choose reliable backup paths (BPs). Then we construct a mathematical model for the failure recovery problem, which takes maximum rerouting traffic as the optimizing objective and the QoS requirements as the constraints. Moreover, we propose a heuristic algorithm for link failure recovery, which adopts the improved k shortest path algorithm to splice the single BP and supplies more protection resources for the links with higher priority. We also prove the correctness of the proposed algorithm. Moreover, the time and space complexity are also analyzed. Simulation results under NS2 show that the proposed algorithm improves the link failure recovery rate and increases the QoS satisfaction rate significantly.

On the Use of Adaptive Weight Functions in Wavelength-Continuous WDM Multi-Fiber Networks under Dynamic Traffic

  • Miliotis Konstantinos V.;Papadimitriou Georgios I.;Pomportsis Andreas S.
    • Journal of Communications and Networks
    • /
    • v.7 no.4
    • /
    • pp.499-508
    • /
    • 2005
  • In this paper, we address the problem of efficient routing and wavelength assignment (RWA) in multi-fiber wavelength division multiplexing (WDM) networks without wavelength translation, under dynamic traffic. We couple Dijkstra's shortest path algorithm with a suitable weight function which chooses optical paths based both on wavelength availability and multi-fiber segments. We compare our approach with other RWA schemes both for regular and irregular WDM multi-fiber network topologies in terms of blocking probability and overall link utilization.

An Algorithm for Searching Pareto Optimal Paths of HAZMAT Transportation: Efficient Vector Labeling Approach (위험물 수송 최적경로 탐색 알고리즘 개발: Efficient Vector Labeling 방법으로)

  • Park, Dong-Joo;Chung, Sung-Bong;Oh, Jeong-Taek
    • Journal of the Korean Society of Hazard Mitigation
    • /
    • v.11 no.3
    • /
    • pp.49-56
    • /
    • 2011
  • This paper deals with a methodology for searching optimal route of hazard material (hazmat) vehicles. When we make a decision of hazmat optimal paths, there is a conflict between the public aspect which wants to minimize risk and the private aspect which has a goal of minimizing travel time. This paper presents Efficient Vector Labeling algorithm as a methodology for searching optimal path of hazmat transportation, which is intrinsically one of the multi-criteria decision making problems. The output of the presented algorithm is a set of Pareto optimal paths considering both risk and travel time at a time. Also, the proposed algorithm is able to identify non-dominated paths which are significantly different from each other in terms of links used. The proposed Efficient Vector Labeling algorithm are applied to test bed network and compared with the existing k-shortest path algorithm. Analysis of result shows that the proposed algorithm is more efficient and advantageous in searching reasonable alternative routes than the existing one.

K-th Path Search Algorithms with the Link Label Correcting (링크표지갱신 다수경로탐색 알고리즘)

  • Lee, Mee-Young;Baik, Nam-Cheol;Choi, Dae-Soon;Shin, Seong-Il
    • Journal of Korean Society of Transportation
    • /
    • v.22 no.2 s.73
    • /
    • pp.131-143
    • /
    • 2004
  • Given a path represented by a sequence of link numbers in a graph, the vine is differentiated from the loop in a sense that any link number can be visited in the path no more than once, while more than once in the loop. The vine provides a proper idea on complicated travel patterns such as U-turn and P-turn witnessed near intersections in urban transportation networks. Application of the link label method(LLM) to the shortest Path algorithms(SPA) enables to take into account these vine travel features. This study aims at expanding the LLM to a K-th path search algorithm (KPSA), which adopts the node-based-label correcting method to find a group of K number of paths. The paths including the vine type of travels are conceptualized as drivers reasonable route choice behaviors(RRCB) based on non-repetition of the same link in the paths, and the link-label-based MPSA is proposed on the basis of the RRCB. The small-scaled network test shows that the algorithm sequence works correctly producing multiple paths satisfying the RRCB. The large-scaled network study detects the solution degeneration (SD) problem in case the number of paths (K) is not sufficient enough, and the (K-1) dimension algorithm is developed to prevent the SD from the 1st path of each link, so that it may be applied as reasonable alternative route information tool, an important requirement of which is if it can generate small number of distinct alternative paths.

Intelligent Optimal Route Planning Based on Context Awareness (상황인식 기반 지능형 최적 경로계획)

  • Lee, Hyun-Jung;Chang, Yong-Sik
    • Asia pacific journal of information systems
    • /
    • v.19 no.2
    • /
    • pp.117-137
    • /
    • 2009
  • Recently, intelligent traffic information systems have enabled people to forecast traffic conditions before hitting the road. These convenient systems operate on the basis of data reflecting current road and traffic conditions as well as distance-based data between locations. Thanks to the rapid development of ubiquitous computing, tremendous context data have become readily available making vehicle route planning easier than ever. Previous research in relation to optimization of vehicle route planning merely focused on finding the optimal distance between locations. Contexts reflecting the road and traffic conditions were then not seriously treated as a way to resolve the optimal routing problems based on distance-based route planning, because this kind of information does not have much significant impact on traffic routing until a a complex traffic situation arises. Further, it was also not easy to take into full account the traffic contexts for resolving optimal routing problems because predicting the dynamic traffic situations was regarded a daunting task. However, with rapid increase in traffic complexity the importance of developing contexts reflecting data related to moving costs has emerged. Hence, this research proposes a framework designed to resolve an optimal route planning problem by taking full account of additional moving cost such as road traffic cost and weather cost, among others. Recent technological development particularly in the ubiquitous computing environment has facilitated the collection of such data. This framework is based on the contexts of time, traffic, and environment, which addresses the following issues. First, we clarify and classify the diverse contexts that affect a vehicle's velocity and estimates the optimization of moving cost based on dynamic programming that accounts for the context cost according to the variance of contexts. Second, the velocity reduction rate is applied to find the optimal route (shortest path) using the context data on the current traffic condition. The velocity reduction rate infers to the degree of possible velocity including moving vehicles' considerable road and traffic contexts, indicating the statistical or experimental data. Knowledge generated in this papercan be referenced by several organizations which deal with road and traffic data. Third, in experimentation, we evaluate the effectiveness of the proposed context-based optimal route (shortest path) between locations by comparing it to the previously used distance-based shortest path. A vehicles' optimal route might change due to its diverse velocity caused by unexpected but potential dynamic situations depending on the road condition. This study includes such context variables as 'road congestion', 'work', 'accident', and 'weather' which can alter the traffic condition. The contexts can affect moving vehicle's velocity on the road. Since these context variables except for 'weather' are related to road conditions, relevant data were provided by the Korea Expressway Corporation. The 'weather'-related data were attained from the Korea Meteorological Administration. The aware contexts are classified contexts causing reduction of vehicles' velocity which determines the velocity reduction rate. To find the optimal route (shortest path), we introduced the velocity reduction rate in the context for calculating a vehicle's velocity reflecting composite contexts when one event synchronizes with another. We then proposed a context-based optimal route (shortest path) algorithm based on the dynamic programming. The algorithm is composed of three steps. In the first initialization step, departure and destination locations are given, and the path step is initialized as 0. In the second step, moving costs including composite contexts into account between locations on path are estimated using the velocity reduction rate by context as increasing path steps. In the third step, the optimal route (shortest path) is retrieved through back-tracking. In the provided research model, we designed a framework to account for context awareness, moving cost estimation (taking both composite and single contexts into account), and optimal route (shortest path) algorithm (based on dynamic programming). Through illustrative experimentation using the Wilcoxon signed rank test, we proved that context-based route planning is much more effective than distance-based route planning., In addition, we found that the optimal solution (shortest paths) through the distance-based route planning might not be optimized in real situation because road condition is very dynamic and unpredictable while affecting most vehicles' moving costs. For further study, while more information is needed for a more accurate estimation of moving vehicles' costs, this study still stands viable in the applications to reduce moving costs by effective route planning. For instance, it could be applied to deliverers' decision making to enhance their decision satisfaction when they meet unpredictable dynamic situations in moving vehicles on the road. Overall, we conclude that taking into account the contexts as a part of costs is a meaningful and sensible approach to in resolving the optimal route problem.

Virtual Network Embedding with Multi-attribute Node Ranking Based on TOPSIS

  • Gon, Shuiqing;Chen, Jing;Zhao, Siyi;Zhu, Qingchao
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.10 no.2
    • /
    • pp.522-541
    • /
    • 2016
  • Network virtualization provides an effective way to overcome the Internet ossification problem. As one of the main challenges in network virtualization, virtual network embedding refers to mapping multiple virtual networks onto a shared substrate network. However, existing heuristic embedding algorithms evaluate the embedding potential of the nodes simply by the product of different resource attributes, which would result in an unbalanced embedding. Furthermore, ignoring the hops of substrate paths that the virtual links would be mapped onto may restrict the ability of the substrate network to accept additional virtual network requests, and lead to low utilization rate of resource. In this paper, we introduce and extend five node attributes that quantify the embedding potential of the nodes from both the local and global views, and adopt the technique for order preference by similarity ideal solution (TOPSIS) to rank the nodes, aiming at balancing different node attributes to increase the utilization rate of resource. Moreover, we propose a novel two-stage virtual network embedding algorithm, which maps the virtual nodes onto the substrate nodes according to the node ranks, and adopts a shortest path-based algorithm to map the virtual links. Simulation results show that the new algorithm significantly increases the long-term average revenue, the long-term revenue to cost ratio and the acceptance ratio.