All previously known efficient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length augmenting paths at once (using the layered network approach of Dinic). An alternative method based

in the problem graph: ( 1) O(n log n + m) for the single-source shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the all-pairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite

We consider the problem of routing traffic to optimize the performance of a congested network. We are given a network, a rate of traffic between each pair of nodes, and a latency function for each edge specifying the time needed to traverse the edge given its congestion; the objective is to route

, reacts faster to important our internai reports on this project [3]-[5]. network changes, and does not suffer from long-term 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

This paper considers the problem of routing connections in a reconfigurable optical network using wavelength division multiplexing, where each connection between a pair of nodes in the network is assigned a path through the network and a wavelength on that path, such that connections whose paths

and space) is a well-studied problem in graph algorithms. We present a simple, novel and generic scheme for all-pairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for all-pairs t-stretch distances for a whole range of stretch t, and also answer

ffi(u, v) < = ^ffi(u, v) < = t * ffi(u, v). The most efficient al-gorithms known for computing small stretch distances in Gare the approximate distance oracles of [16] and the three algorithms in [9] to compute all-pairs stretch t distancesfor t = 2, 7/3, and 3. We present faster algorithms

In this paper, we study the problems of enumerating cuts of a graph by non-decreasing weights. There are four problems, depending on whether the graph is directed or undirected, and on whether we consider all cuts of the graph or only s-t cuts for a given pair of vertices s,t. Efficient

algorithm APASP 2 for computing all distances in G with an additive one-sided 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

The upper bound on the exponent, ω, of matrix multiplication over a ring that was three in 1968 has decreased several times and since 1986 it has been 2.376. On the other hand, the exponent of the algorithms known for the all pairs shortest path problem has stayed at three all these years even