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137
The New Routing Algorithm for the ARPANET
 IEEE Transactions on Communications
, 1980
"... AbsrracrThe new ARPANET routing algorithm is an improvement test results. This paper is a summary of our conclusions only; over the old procedure in that it uses fewer network resources, operates on for more complete descriptions of our research findings, see more realistic estimates of network con ..."
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Cited by 266 (2 self)
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AbsrracrThe new ARPANET routing algorithm is an improvement test results. This paper is a summary of our conclusions only; over the old procedure in that it uses fewer network resources, operates on for more complete descriptions of our research findings, see more realistic estimates of network conditions, reacts faster to important our internai reports on this project [3][5]. network changes, and does not suffer from longterm loops or oscillations. In the new procedure, each node in the network maintains a database 11. PROBLEMS WITH THE ORIGINAL ALGORITHM describing the complete network topology and the delays on all lines, and uses the database describing the network to generate a tree representing the me original ARPANET routing algorithm and the new verminimum delay paths from a given root node to every other network node. sion both attempt to route packets along paths of least delay. Because the traffic in the network can be quite variable, each node The total path is not determined in advance; rather, each node periodically measures the delays along its outgoing lines and forwards this decides which line to use in forwarding the packet to the next information to all other nodes. The delay information propagates quickly through the network so that all nodes can update their databases and node. In the original approach, each node maintained a table continue to route traffic in a consistent and efficient manner. An extensive series of tests were conducted on the ARPANET, showing that line overhead and CPU overhead are 60th less than two percent, most nodes learn of an update within 100 ms, and the algorithm detects congestion and routes packets around congested areas. T I.
Faster algorithms for the shortest path problem
, 1990
"... Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, mn edges, and nonnegative integer arc costs bounded by C, a onelevel form of radix heap gives a time b ..."
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Cited by 104 (10 self)
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Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, mn edges, and nonnegative integer arc costs bounded by C, a onelevel form of radix heap gives a time bound for Dijkstra's algorithm of O(m + n log C). A twolevel form of radix heap gives a bound of O(m + n log C/log log C). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O(m + n /log C). The best previously known bounds are O(m + n log n) using Fibonacci heaps alone and O(m log log C) using the priority queue structure of Van Emde Boas et al. [17].
All Pairs Almost Shortest Paths
 SIAM Journal on Computing
, 1996
"... Let G = (V; E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive onesided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe g) time ..."
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Cited by 83 (8 self)
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Let G = (V; E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive onesided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe g) time algorithm APASP 2 for computing all distances in G with an additive onesided error of at most 2. The algorithm APASP 2 is simple, easy to implement, and faster than the fastest known matrix multiplication algorithm. Furthermore, for every even k ? 2, we describe an g) time algorithm APASP k for computing all distances in G with an additive onesided error of at most k.
Finding the Hidden Path: Time Bounds for AllPairs Shortest Paths
, 1993
"... We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra's ..."
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Cited by 64 (0 self)
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We investigate the allpairs shortest paths problem in weighted graphs. We present an algorithmthe Hidden Paths Algorithmthat finds these paths in time O(m* n+n² log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra's algorithm. We argue that m* is likely to be small in practice, since m* = O(n log n) with high probability for many probability distributions on edge weights. We also prove an Ω(mn) lower bound on the running time of any pathcomparison based algorithm for the allpairs shortest paths problem. Pathcomparison based algorithms form a natural class containing the Hidden Paths Algorithm, as well as the algorithms of Dijkstra and Floyd. Lastly, we consider generalized forms of the shortest paths problem, and show that many of the standard shortest paths algorithms are effective in this more general setting.
All Pairs Shortest Paths using Bridging Sets and Rectangular Matrix Multiplication
 Journal of the ACM
, 2000
"... We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves... ..."
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Cited by 60 (6 self)
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We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves...
Scaling Algorithms for Network Problems
, 1985
"... This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a b ..."
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Cited by 59 (2 self)
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This paper gives algorithms for network problems that work by scaling the numeric parameters. Assume all parameters are integers. Let n, m, and N denote the number of vertices, number of edges, and largest parameter of the network, respectively. A scaling algorithm for maximum weight matching on a bipartite graph runs in O(n3 % log N) time. For appropriate N this improves the traditional Hungarian method, whose most efftcient implementation is O(n(m + n log n)). The speedup results from finding augmenting paths in batches. The matching algorithm gives similar improvements for the following problems: singlesource shortest paths for arbitrary edge lengths (Bellman’s algorithm); maximum weight degreeconstrained subgraph; minimum cost flow on a cl network. Scaling gives a simple maximum value flow algorithm that matches the best known bound (Sleator and Tarjan’s algorithm) when log N = O(log n). Scaling also gives a good algorithm for shortest paths on a directed graph with nonnegative edge lengths (Dijkstra’s algorithm).
Exact and Approximate Distances in Graphs  a survey
 In ESA
, 2001
"... We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems. ..."
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Cited by 57 (0 self)
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We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems.
Optimizing TwoPhase, LevelClocked Circuitry (Extended Abstract)
"... We investigate two strategies for reducing the clock period of a twophase, levelclocked circuit: clock tuning, which adjusts the waveforms that clock the circuit, and retiming, which relocates circuit latches. These methods can be used to convert a circuit with edgetriggered latches into a faster ..."
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Cited by 55 (16 self)
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We investigate two strategies for reducing the clock period of a twophase, levelclocked circuit: clock tuning, which adjusts the waveforms that clock the circuit, and retiming, which relocates circuit latches. These methods can be used to convert a circuit with edgetriggered latches into a faster levelclocked one. We model a twophase circuit as a graph whose vertex set V is a collection of combinational logic blocks, and whose edge set E is a set of interconnections. Each interconnection passes through 0 or more latches, where each latch is clocked by one of two periodic, nonoverlapping waveforms, or phases. We give efficient polynomialtime algorithms for problems involving the timing verification and optimization of twophase circuitry. Included are algorithms for ffl verifyi...