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All-Pairs Shortest Paths in O(n²) Time with High Probability

Yuval Peres, Dmitry Sotnikov, Benny Sudakov, Uri Zwick
2010 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
in expectation and with high probability.  ...  The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n 2 ), in expectation and with high probability.  ...  Furthermore, our algorithm runs in O(n 2 ) time with high probability and works for both directed and undirected versions of the all-pairs shortest paths problem.  ...

All-pairs shortest paths inO(n2) time with high probability

Yuval Peres, Dmitry Sotnikov, Benny Sudakov, Uri Zwick
2013 Journal of the ACM
in expectation and with high probability.  ...  The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n 2 ), in expectation and with high probability.  ...  Furthermore, our algorithm runs in O(n 2 ) time with high probability and works for both directed and undirected versions of the all-pairs shortest paths problem.  ...

Faster Walks in Graphs: AÕ(n2) Time-Space Trade-off for Undirecteds-tConnectivity [chapter]

2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
As our main result, we propose a family of randomized algorithms for USTCON which achieves a time-space product of S·T = O(n 2 ) in graphs with n nodes and m edges (where the O-notation disregards poly-logarithmic  ...  In particular, we obtain an algorithm running in time O(n + m) which is, in general, more space-efficient than both BFS and DFS.  ...  Since the path P s = (i 0 , i 1 , . . . , i a−1 ) is a shortest path in graph G between nodes i 0 and i a−1 , such that P s ⊆ A and Γ(P s ) ⊆ A, it follows that (cf.  ...

Optimality Bounds of the Connectivity of Adhoc Networks with Beamforming Antennas

Moritz Kiese, Christian Hartmann, Robert Vilzmann
2009 GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference
Adhoc networks will play an important role in future access networks. Previous studies have shown, that the connectivity of such networks can be notably increased by employing directional antennas.  ...  This work tries to close this gap by providing a method to calculate provable bounds on the connectivity of an adhoc network with keyhole antennas and a variety of secondary optimization criteria via Mixed  ...  Finding these paths can be interpreted as a classic shortest path problem (solvable by polynomial algorithms like Dijkstra's Algorithm  ), with link weights σ e : If the total cost of the shortest  ...

Edge-disjoint paths revisited

Chandra Chekuri, Sanjeev Khanna
2007 ACM Transactions on Algorithms
The approximability of the maximum edge disjoint paths problem (EDP) in directed graphs was seemingly settled by the fl(ml/2-e)-hardness result of Guruswami et al.  and the O(x/~ ) approximation achievable  ...  Our results also extend to EDP with weights and to the unsplittable flow problem with uniform edge capacities.  ...  The algorithm simply considers the shortest path length for each unrouted (si, ti) pair and connects a pair with minimum shortest path length via its shortest path.  ...

Page 5784 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews
: time bounds for all-pairs shortest paths.  ...  Summary: “The all-pairs shortest-paths problem in weighted graphs is investigated.  ...

A new algorithm to find the shortest paths between all pairs of nodes

G. Gallo, S. Pallottino
1982 Discrete Applied Mathematics
A new algorithm to find the shortest paths between all pairs of nodes is presented. This algorithm makes use of a dual cost transformation and of a particular data structure.  ...  Its worst case time complexity is of the order of the third power of the number of nodes, and its space complexity is linear with the number of arcs.  ...  In such models usually the shortest paths between all Origin-Destination pairs need to be determined many times, with different values of arc lengths.  ...

Shortest path problems with node failures

Patrick Jaillet
1992 Networks
Consider the problem of finding the shortest paths from a node source s to a node sink t in a complete network.  ...  We first show that the problem is, in general, NPhard and then we develop polynomial time procedures for special cases of it.  ...  the path with maximum probability of being the shortest, or finding the path with minimum variance among the shortest, etc.  ...

Monitoring path nearest neighbor in road networks

Zaiben Chen, Heng Tao Shen, Xiaofang Zhou, Jeffrey Xu Yu
2009 Proceedings of the 35th SIGMOD international conference on Management of data - SIGMOD '09
In the searching phase, the BNE finds the shortest path to the destination, during which a candidate set that guarantees to include the k -PNN is generated at the same time.  ...  Given a destination where a user is going to, this new query returns the k -NN with respect to the shortest path connecting the destination and the user's current location, and thus provides a list of  ...  High deviation implies that the user usually does not choose the shortest path and an update of the whole k -PNN is required each time the user deviates.  ...

Performance evaluation of ATM shortcut connections in overlaid IP/ATM networks

V. Firoiu, J. Kurose, D. Towsley
1999 IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320)
These experiments indicate that in many cases the utilization of an IP/ATM network increases proportionally to the decrease in the average path length when ATM shortcuts are used.  ...  We model an IP/ATM network with and without ATM shortcuts as two loss networks.  ...  The 1P tlows can be routed in two ways: one is over the shortest path in the 1P network following the path of each 1P link in the ATM network; the other is over the shortest path in ATM network (i.e.,  ...

Local Link Protection Scheme in IP Networks [chapter]

Hui-Kai Su, Cheng-Shong Wu
2007 Lecture Notes in Computer Science
In this paper, we proposed an IP Local Link-Protection (IPLLP) scheme based on the characteristic of shortest-path routing in IP networks.  ...  In the simulation results, we observe that IP Local Link-Protection scheme can efficiently improve network survivability in a small-scale and high-degree network.  ...  Second, all scenarios of each link failure are simulated, and all O-D pairs are tested according to the present routing tables.  ...

David P. Woodruff
2010 Lecture Notes in Computer Science
With probability ≥ 1 − 1/n, H is an additive (2k + 4 )-spanner. Proof. Fix a pair {a, b} of vertices in G and a shortest path P between them.  ...  Fix a pair {a, b} of vertices in G, and fix any shortest path P from a to b in G with the fewest heavy edges.  ...

Resource discovery in distributed networks

Mor Harchol-Balter, Tom Leighton, Daniel Lewin
1999 Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing - PODC '99
The total number of connections required is O(n log2 n) and the total number of pointers which must be communicated is O(n2 log2 n), with high probability.  ...  We propose a very simple algorithm called Name-Dropper whereby all machines learn about each other within O(log' n) rounds with high probability, where n is the number of machines in the network.  ...  Then we're done by the following argument: Pick one shortest path between each of the n2 pairs of nodes. Each of these shortest paths has at most n triples.  ...

Packet Routing with Genetically Programmed Mobile Agents [chapter]

Jon Schuringa, Günter Remsak
2000 Telecommunication Network Intelligence
The result is a high performance, self-configuring routing method, irrespective of the network topology and traffic.  ...  We use genetic programming to build mobile agents that monitor the network status and set the routing tables in the network nodes in such a way that it maximizes network throughput and minimizes the overall  ...  To compute the shortest path between all pairs has computational complexity O(N2).  ...

Designing stimulating programming assignments for an algorithms course

Michael Mitzenmacher
1996 ACM SIGCSE Bulletin
Specifically, we provide problems for algorithms that compute minimum spanning trees, connected components, maximum flows, and all-pairs shortest paths.  ...  Here we demonstrate how some of these results can be used to develop stimulating, open-ended exercises for courses in algorithms and data structures or graph theory.  ...  weight spanning tree, connected components, maximum flow, and all-pairs shortest paths.  ...
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