S. Pallottino. Shortest-Path Methods: Complexity, Interrelations and New Propositions. Networks, 14:257-267, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....n nodes and m = O(n) edges and random edge weights such that the Bellman Ford algorithm with a FIFO queue requires (n 4=3 ) operations whp for any constant 0 1=3. The above input class also yields poor performance on other SSSP label correcting approaches like Pallottino s algorithm [21] which has worst case execution time O(n 2 m) but performs very well on many practical inputs [4, 27] Pallottino s algorithm maintains two FIFO queues Q 1 and Q 2 . The next node to be removed is taken from the head of Q 1 if this queue is not empty and from the head of Q 2 otherwise. A node ....

S. Pallottino. Shortest-path methods: Complexity, interrelations and new propositions. Networks, 14:257{ 267, 1984.

....and m arcs. This is the best currently known strongly polynomial bound for the problem (see [6] for the best weakly polynomial bound) In practice, however, the Bellman Ford algorithm is usually outperformed by the deque algorithm of D Escopo Pape [9] and by the two queue algorithm of Pallottino [8]. The workcase time bounds for these algorithms, however, are worse than those for the Bellman Ford algorithm. The deque algorithm may take exponential time in the worst case [10] and the two queue algorithm may take Omega Gamma n 2 m) time. We propose a new topological scan algorithm for the ....

S. Pallottino. Shortest-Path Methods: Complexity, Interrelations and New Propositions. Networks, 14:257--267, 1984.

....[3, 9, 21] These researchers are attributed with the first polynomially bounded label correcting algorithm, which has a worst case behavior of O(nm) In this paper, we refer to this algorithm as the one queue algorithm. A variant of this algorithm by Pallottino uses two queues to store the list[22, 23]. If a node has been seen before, it is put in the first queue; otherwise, it is put in the second. Nodes are removed first from the first queue, then the second queue. The idea of the algorithm is that nodes that have been seen and updated already should be updated again before nodes that have ....

S. Pallottino. Shortest-path methods: Complexity, interrelations and new propositions. Networks, 14:257--267, 1984.

....work was done while the author was visiting NEC Research Institute, Inc. 1 Introduction The negative cycle problem is the problem of finding a negative length cycle in a network or proving that there are none (see e.g. 15] The problem is closely related to the shortest path problem (see e.g. [1, 7, 16, 18, 19, 20]) of finding shortest path distances in a network with no negative cycles. The negative cycle problem comes up both directly, for example in currency arbitrage, and as a subproblem in algorithms for other network problems, for example the minimum cost flow problem [14] The best theoretical time ....

....for many practical situations. The previously known shortest path algorithms we study are the classical Bellman Ford Moore algorithm; the Goldberg Radzik algorithm [12] which on shortest path problems per1 formed very well in a previous study [2] an incremental graph algorithm of Pallottino [19], which performs well on some classes of shortest path problems; and an algorithm of Tarjan [21] which is a combination of the Bellman Ford Moore algorithm and a subtree disassembly strategy for cycle detection. We also study several new algorithm variations. We develop a version of the network ....

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S. Pallottino. Shortest-Path Methods: Complexity, Interrelations and New Propositions. Networks, 14:257--267, 1984.

....investigation of available algorithms. In particular, a massive study of flow and matching algorithms was done for the First DIMACS Algorithm Implementation Challenge [15] In this paper we study practical performance of several shortest paths algorithms, including established methods [2, 6, 7, 11, 18, 19, 20, 21], recently proposed algorithms [1, 14] and new algorithms. The development of the new algorithms was based on the experimental feedback. We give theoretical explanation of the observed behavior of the algorithms and prove complexity bounds on the new algorithms. We also prove an interesting ....

....bounds for this variant of Dijkstra s algorithm on networks with arbitrary arc lengths. 10 4.3. Incremental Graph Algorithms. In this section we describe two algorithms. The first one was developed independently by Pape [21] and Levit [18] The second algorithm was proposed by Pallottino [20]. He also introduced the incremental graph framework that unified these two algorithms. Our implementations of the above algorithms are called pape, and two q, respectively. An algorithm in the restricted scan framework maintains a set W of nodes and scans only labeled nodes in W . The set W is ....

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S. Pallottino. Shortest-Path Methods: Complexity, Interrelations and New Propositions. Networks, 14:257--267, 1984.

....cost arcs. Two lists connected in series Algorithms in this family try to anticipate, when compared to a plain FIFO policy, the updating of inexact labels of the nodes currently in Q before they are actually scanned. Lists with two insertion points have been proposed for this purpose in [22, 25, 26]. In these algorithms, Q can be viewed as two lists Q and Q where selection is made from the head of Q (from the head of Q whether Q = while insertion can be made either in Q or in Q . Since inexact labels may arise only once a node has been inserted into Q more than once, in algorithm ....

....Q is used as a stack while Q is used as a queue and contains each node at most once. The stack nature of Q is the cause of the exponential time complexity, O(n2 n ) 21] in fact, it is possible that a node is selected and scanned 2 n 2 times in the same pass. The variant proposed in [25] is based on the implementation of Q as a queue, where nodes are reinserted at the tail of Q . The resulting algorithm, called SPT L 2queue, results to be polynomial, O(mn 2 ) since a node can be selected and scanned no more than n times in the same pass. A double insertion policy, that is a ....

S. Pallottino, Shortest-path methods: complexity, interrelations and new propositions, Networks 14 (1984) 257267.

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S. Pallottino. Shortest-Path Methods: Complexity, Interrelations and New Propositions. Networks, 14:257-267, 1984.

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S. Pallottino. Shortest-path methods: Complexity, interrelations and new propositions. Networks, 14:257--267, 1984.

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S. Pallottino. Shortest-path methods: Complexity, interrelations and new propositions. Networks, 14:257--267, 1984.

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