New dynamic algorithms for shortest path tree computation
TL;DR: An algorithmic framework is established that allows for a variety of dynamic SPT algorithms including dynamic versions of the well-known Dijkstra, Bellman-Ford, D'Esopo-Pape algorithms, and to establish proofs of correctness for these algorithms in a unified way.
Abstract: The open shortest path first (OSPF) and IS-IS routing protocols widely used in today's Internet compute a shortest path tree (SPT) from each router to other routers in a routing area Many existing commercial routers recompute an SPT from scratch following changes in the link states of the network Such recomputation of an entire SPT is inefficient and may consume a considerable amount of CPU time Moreover, as there may coexist multiple SPTs in a network with a set of given link states, recomputation from scratch causes frequent unnecessary changes in the topology of an existing SPT and may lead to routing instability We present new dynamic SPT algorithms that make use of the structure of the previously computed SPT Besides efficiency, our algorithm design objective is to achieve routing stability by making minimum changes to the topology of an existing SPT (while maintaining shortest path property) when some link states in the network have changed We establish an algorithmic framework that allows us to characterize a variety of dynamic SPT algorithms including dynamic versions of the well-known Dijkstra, Bellman-Ford, D'Esopo-Pape algorithms, and to establish proofs of correctness for these algorithms in a unified way The theoretical asymptotic complexity of our new dynamic algorithms matches the best known results in the literature
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TL;DR: LPA* is developed, an incremental version of A* that combines ideas from the artificial intelligence and the algorithms literature and repeatedly finds shortest paths from a given start vertex to a given goal vertex while the edge costs of a graph change or vertices are added or deleted.
584 citations
Cites methods from "New dynamic algorithms for shortest..."
...For example, in “most of today’s commercial routers, this recomputation is done by deleting the current SPT [shortest-path tree] and recomputing it from scratch by using the well known Dijkstra algorithm” [12] although it has recently been discovered in the networking literature that DynamicSWSF-FP can be used to update routing tables as the congestion of links changes [12,13]....
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TL;DR: In this article, the authors proposed receding horizon control (RHC) as a straightforward method for designing feedback controllers that deliver good performance while respecting complex constraints, such as the objective, constraints, prediction method, and horizon.
Abstract: In this article we have shown that receding horizon control offers a straightforward method for designing feedback controllers that deliver good performance while respecting complex constraints. A designer specifies the RHC controller by specifying the objective, constraints, prediction method, and horizon, each of which has a natural choice suggested directly by the application. In more traditional approaches, such as PID control, a designer tunes the controller coefficients, often using trial and error, to handle the objectives and constraints indirectly. In contrast, RHC con trollers can often obtain good performance with little tuning. In addition to the straightforward design process, we have seen that RHC controllers can be implemented in real time at kilohertz sampling rates. These speeds are useful for both real-time implementation of the controller as well as rapid Monte Carlo simulation for design and testing purposes. Thus, receding horizon control can no longer be considered a slow, computationally intensive policy. Indeed, RHC can be applied to a wide range of control problems, including applications involving fast dynamics.
379 citations
Cites background from "New dynamic algorithms for shortest..."
...Note that the LP solution includes the visibility information on all pairs of nodes for all the obstacles, which allows for a fast incremental update of the visibility graph when the environment changes [83, 84]....
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TL;DR: An incremental version of ISOMAP, one of the key manifold learning algorithms, is described and it is demonstrated that this modified algorithm can maintain an accurate low-dimensional representation of the data in an efficient manner.
Abstract: Understanding the structure of multidimensional patterns, especially in unsupervised cases, is of fundamental importance in data mining, pattern recognition, and machine learning. Several algorithms have been proposed to analyze the structure of high-dimensional data based on the notion of manifold learning. These algorithms have been used to extract the intrinsic characteristics of different types of high-dimensional data by performing nonlinear dimensionality reduction. Most of these algorithms operate in a "batch" mode and cannot be efficiently applied when data are collected sequentially. In this paper, we describe an incremental version of ISOMAP, one of the key manifold learning algorithms. Our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low-dimensional representation of the data in an efficient manner.
289 citations
Additional excerpts
...Several algorithms have been proposed to analyze the structure of highdimensional data based on the notion of manifold learning....
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Patent•
24 Jun 2002
TL;DR: In this paper, the present invention relates to dynamic discovery of documents or information through a focused crawler or search engine, and it pertains to the field of computer software development.
Abstract: The present invention pertains to the field of computer software. More specifically, the present invention relates to dynamic discovery of documents or information through a focused crawler or search engine.
284 citations
25 Mar 2008
TL;DR: This paper proposes a novel algorithm to find the minimum-travel-time path with the best departure time for a LTT(vs, v query over a large graph, which outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice.
Abstract: The spatial and temporal databases have been studied widely and intensively over years. In this paper, we study how to answer queries of finding the best departure time that minimizes the total travel time from a place to another, over a road network, where the traffic conditions dynamically change from time to time. We study a generalized form of this problem, called the time-dependent shortest-path problem. A time-dependent graph GT is a graph that has an edge-delay function, wi, j(t), associated with each edge (vi, vj), to be stored in a database. The edge-delay function wi, j(t) specifies how much time it takes to travel from node vi to node vj, if it departs from vi at time t. A user-specified query is to ask the minimum-travel-time path, from a source node, vs, to a destination node, ve, over the time-dependent graph, GT, with the best departure time to be selected from a time interval T. We denote this user query as LTT(vs, ve, T) over GT. The challenge of this problem is the added complexity due to the time dependency in the time-dependent graph. That is, edge delays are not constants, and can vary from time to time. In this paper, we propose a novel algorithm to find the minimum-travel-time path with the best departure time for a LTT(vs, ve, T) query over a large graph GT. Our approach outperforms existing algorithms in terms of both time complexity in theory and efficiency in practice. We will discuss the design of our algorithm, together with its correctness and complexity. We conducted extensive experimental studies over large graphs and will report our findings.
252 citations
Cites background from "New dynamic algorithms for shortest..."
...The variations of single-source shortest-path problem and related issues have been intensively studied in the areas of transportation [15, 12, 13, 17, 2, 29, 21], navigation systems [24, 14, 3, 9], and networks [18, 19]....
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References
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TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Abstract: We consider n points (nodes), some or all pairs of which are connected by a branch; the length of each branch is given. We restrict ourselves to the case where at least one path exists between any two nodes. We now consider two problems. Problem 1. Constrnct the tree of minimum total length between the n nodes. (A tree is a graph with one and only one path between every two nodes.) In the course of the construction that we present here, the branches are subdivided into three sets: I. the branches definitely assignec~ to the tree under construction (they will form a subtree) ; II. the branches from which the next branch to be added to set I, will be selected ; III. the remaining branches (rejected or not yet considered). The nodes are subdivided into two sets: A. the nodes connected by the branches of set I, B. the remaining nodes (one and only one branch of set II will lead to each of these nodes), We start the construction by choosing an arbitrary node as the only member of set A, and by placing all branches that end in this node in set II. To start with, set I is empty. From then onwards we perform the following two steps repeatedly. Step 1. The shortest branch of set II is removed from this set and added to
22,704 citations
"New dynamic algorithms for shortest..." refers methods in this paper
...When the static version of the initialization procedure is used, this algorithm is equivalent to the Dijkstra algorithm [ 7 ]....
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...In most of today’s commercial routers, this recomputation is done by deleting the current SPT and recomputing it from scratch by using the well-known Dijkstra algorithm [ 7 ]....
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Book•
01 Jan 1990TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Abstract: From the Publisher:
The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects.
In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage.
As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds.
Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.
21,651 citations
"New dynamic algorithms for shortest..." refers methods or result in this paper
...The Fibonacci Dijkstra algorithm uses the data structure of a Fibonacci heap to implement the priority queue for . Although the algorithm has the lowest asymptotic complexity among others shown above, it is mostly of theoretical interest because of the large constant overhead involved in operating Fibonacci heaps [ 5 ]....
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...For comparison with the well-known static algorithms, we state the following known results regarding their complexity [ 5 ]:...
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TL;DR: Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, the functional equation technique of dynamic programming and approximation in policy space yield an iterative algorithm which converges after at most (N-1) iterations.
Abstract: : Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, we wish to determine the path from one given city to another given city which minimizes the travel time. The times are not directly proportional to the distances due to varying quality of roads, and v varying quantities of traffic. The functional equation technique of dynamic programming, combined with approximation in policy space, yield an iterative algorithm which converges after at most (N-1) iterations.
2,586 citations
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01 Apr 1998
TL;DR: This memo documents version 2 of the OSPF protocol, a link-state routing protocol designed to be run internal to a single Autonomous System.
Abstract: This memo documents version 2 of the OSPF protocol. OSPF is a link-state routing protocol. It is designed to be run internal to a single Autonomous System. Each OSPF router maintains an identical database describing the Autonomous System's topology. From this database, a routing table is calculated by constructing a shortest- path tree.
2,413 citations
TL;DR: In this paper, the authors specify extensions to two common internetwork routing algorithms (distancevector routing and link-state routing) to support low-delay datagram multicasting beyond a single LAN, and discuss how the use of multicast scope control and hierarchical multicast routing allows the multicast service to scale up to large internetworks.
Abstract: Multicasting, the transmission of a packet to a group of hosts, is an important service for improving the efficiency and robustness of distributed systems and applications. Although multicast capability is available and widely used in local area networks, when those LANs are interconnected by store-and-forward routers, the multicast service is usually not offered across the resulting internetwork. To address this limitation, we specify extensions to two common internetwork routing algorithms—distance-vector routing and link-state routing—to support low-delay datagram multicasting beyond a single LAN. We also describe modifications to the single-spanning-tree routing algorithm commonly used by link-layer bridges, to reduce the costs of multicasting in large extended LANs. Finally, we discuss how the use of multicast scope control and hierarchical multicast routing allows the multicast service to scale up to large internetworks.
1,365 citations