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We consider the reliable transmission of messages via quickest paths in a network with bandwidth, delay and reliability parameters
specified for each link. For a message of size σ, we present algorithms to compute all-pairs quickest most-reliable and most-reliable
quickest paths each with time complexity O(n
2
m), where n and m are the number of nodes and links of the network, respectively.

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you can request a copy directly from the authors.

... In this case, it is of interest to consider the reliabilities of quickest paths. Polynomial time algorithms have been proposed for the quickest most-reliable and the most-reliable quickest path problems in [32] and for all-pairs quickest most-reliable and allpairs most-reliable quickest path problems in [1]. In [30], pseudo polynomial exact methods and fully polynomial approximation methods were proposed to find a quickest path among those with at least a prefixed reliability. ...

... In this case, it is of interest to consider the reliabilities of quickest paths. Polynomial time algorithms have been proposed for the quickest most-reliable and the most-reliable quickest path problems in [32] and for all-pairs quickest most-reliable and allpairs most-reliable quickest path problems in [1]. In [30], pseudo polynomial exact methods and fully polynomial approximation methods were proposed to find a quickest path among those with at least a prefixed reliability. ...

In this paper we consider the evaluation of the probability that a stochastic flow network allows the transmission of a given amount of flow through one path, connecting the source and the sink node, within a fixed amount of time. This problem, called the quickest path flow network reliability problem, belongs to the NP-hard family. This implies that no polynomial algorithm is known for solving it exactly in a CPU runtime bounded by a polynomial function of the network size. As an alternative, we propose to perform estimations by a Monte-Carlo simulation method. We illustrate that the proposed tool evaluates, with high precision and within small CPU runtime, configurations which cannot be handled, in reasonable CPU runtime, by means of a well-known exact method.

The quickest path problem deals with the transmission of a message of size {sigma} from a source to a destination with the minimum end-to-end delay over a network with bandwidth and delay constraints on the links. We consider four basic modes and two variations for the message delivery at the nodes reacting the mechanisms such as circuit switching, Internet protocol, and their combinations. For each of first three modes, we present O(m{sup 2} + mn log n) time algorithm to compute the quickest path for a given message size {sigma}. For the last mode, the quickest path can be computed in O(m + n log n) time.

In a number of distributed computing applications, messages must be transmitted on demand between processes running at different locations on the Internet. The end-to-end delays experienced by the messages have a significant “random” component due to the complicated nature of network traffic. We propose a method based on delay-regression estimation to achieve low end-to-end delays for message transmissions in distributed computing applications. Two-paths are realized between various communicating processes in a transparent manner. Our scheme is implemented over the Internet by a network of NetLets, which communicate with one another to maintain an accurate “state” of delay-regressions in the network. NetLets handle all network traffic between the processes and also perform routing at a certain level depending on the underlying network. We present experimental results to illustrate that NetLets provide a viable and practical means for achieving low end-to-end delays for distributed computing applications over the Internet.

The quickest path problem deals with the transmission of a message of size σ from a source to a destination with the minimum end-to-end delay over a network with bandwidth and delay constraints on the links. The path-table that maps all intervals for σ to the corresponding quickest paths can be computed in time, where n and m are the number of nodes and links of the network, respectively. We propose linear-time algorithms that update the path-table after a increase or decrease bandwidth of a link or a path, respectively.

Flows of convoy-type traffic through networks whose arcs are characterized by both travel times and flowrate constraints are investigated. Suggested, in particular, is the notion of a 'flowrate-constrained fastest path' - a path by means of which the entirety of a volume of traffic, initially located at a source node, can arrive at a sink in as short a time as possible when all traffic must flow along the same path and rates of flow along arcs are limited by flowrate constraints. Several theorems about flowrate-constrained fastest times and paths are stated and proved; it is shown that such paths are independent of source volume whenever this volume is sufficiently large. Two algorithms for finding flowrate-constrained fastest times and paths are given. 8 refs. iliwe fycfnoor-ty eotsarfictt. Several theorems about flowrate-constrained fastest times and paths are saeeb nnt arnvsda etiiv siwa eh. Ssgce tthse independent of source volume whenever this volume is sufficiently large. Two algorithms for finding flowrate-constrained fastest times and paths are given.

Let N be an input network and σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N such that the time required to ship σ units of data from the source to the sink is minimum. When the value of σ is given, an O(m2 + nm log m) algorithm is designed to find the quickest path, where m and n are the numbers of arcs and nodes in the network N, respectively. By generalizing this algorithm properly, a more general algorithm with similar time complexity is developed to find quickest paths for all possible values of σ. Using the algorithm, the values of σ can be divided into O(m) ordered regions such that each region has a corresponding quickest path; therefore, if the general algorithm is used as a preprocessing step to handle the input network N, then the problem of finding a quickest path for a given value of σ can be solved in time O(log m).

Let N = (V, A, c, l) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function l. Let σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n), where n = ¦V¦, e = ¦A¦, and r is the number of distinct capacity values of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space requirement. We then study the constrained quickest path problem and propose an O(re + rn log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rmn2 log n).

Let N be an input network and σ be the amount of data to be transmitted. We present an O(mn2) time algorithm that finds all-pairs quickest paths, for a given value of σ, and show that the quickest path between any two nodes for any value of σ can be found in O(log m) time, provided O(mn2) preprocessing time is spent.

We consider the transmission of a message of size r from a source to adestination over a computer network with n nodes and m links. There are three sources of delays for a message transmitted over the network: (a) propagation delays along the links, (b) delays due to the bandwidth availability on the links, and (c) queuing delays at the intermediate nodes. If the delay in (b) is a non-increasing function of the bandwidth, we propose an O(m2 + mn log n) time algorithm to compute a path with the minimum end-to-end delay for a given message. For the general case, we show the size of path-table to be infinite. Under the condition that the delay curves are continuous and intersect with each other in no more than τ connected regions, we show that path-table size has as an upper bound the Davenport-Schinzelnumber λs(ρ*), where ρ* is the dominant path number of G. We also discuss special cases where the path-table is of significantly smaller size.

Routing in the newer generation of network transmission methods may be performed at various levels of the IP stack such as datagram, TCP stream, and application levels. It is important in the use of these methods to compute the routes that minimize the end-to-end delays for the specific routing mechanism. We formulate an abstract network path computation problem, the dynamic quickest path problem, to encompass a number of message forwarding mechanisms including circuit switching, Internet Protocol, and their variations. This problem deals with the transmission of a message from a source to a destination with the minimum end-to-end delay over a network with propagation delays and dynamic bandwidth constraints on the links. The available bandwidth for each link is specified as a piecewise constant function. We present for each message forwarding mechanism or mode an algorithm to compute a path with the minimum end-to-end delay for a given message size. Our algorithms with suitable network restrictions have polynomial time complexity in the size of the network and total number of segments in the bandwidth list.

In this paper we discuss the quickest path problem and proposed an θ(λn 2 ) space data structure which allows to answer quickest path queries in O(log r) time and whose construction requires θ(min {mn 2 , rn 2 log n+rnm}) time

Let N=(V,E,c,l,p) be a network where V is the set of n vertices, E is the set of m edges, c(u,v)/spl ges/0 is the capacity of edge {u,v}, l(u,v)/spl ges/0 is the delay of edge {u,v}, p(u,v)/spl isin/[0,1] is the operational probability of edge {u,v}. In this letter, we present O(rm+rnlog n) time algorithms for the most reliable quickest path problem and the quickest most reliable path problem, where r is the number of different capacity values in the network.

We consider the transmission of a message of size r from a source to a destination with the minimum end-to-end delay over a computer network where bandwidth can be reserved and guaranteed on the links. Different paths will be required for different intervals of values for r. We propose a polynomial-time algorithm that computes a table that maps all intervals for r to the corresponding paths that minimize the end-to-end delay.