Two Techniques For Fast Computation Computer Science Essay


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Computing constrained shortest paths is fundamental to some important network functions such as QoS routing, MPLS path selection, ATM circuit routing, and traffic engineering. The problem is to find the cheapest path that satisfies certain constraints. In particular, finding the cheapest delay-constrained path is critical for real-time data flows such as voice/video calls. Because it is NP-complete, much research has been designing heuristic algorithms that solve the -approximation of the problem with an adjustable accuracy. A common approach is to discretize (i.e., scale and round) the link delay or link cost, which transforms the original problem to a simpler one solvable in polynomial time. The efficiency of the algorithms directly relates to the magnitude of the errors introduced during discretization. In this paper, we propose two techniques that reduce the discretization errors, which allow faster algorithms to be designed. Reducing the overhead of computing constrained shortest paths is practically important for the successful design of a high-throughput QoS router, which is limited at both processing power and memory space. Our simulations show that the new algorithms reduce the execution time by an order of magnitude on power-law topologies with 1000 nodes. The reduction in memory space is similar.

2.1. Introduction

A fundamental problem that underlies many important network functions such as QoS routing, path selection, and traffic engineering, is to find the constrained shortest path the cheapest path that satisfies a set of constraints. For interactive real-time traffic, the delay constrained least-cost path has particular importance. It is the cheapest path whose end to-end delay is bounded by the delay requirement of a time-sensitive data flow. The additional bandwidth requirement, if there is one, can be easily handled by a pre processing step that prunes the links without the required bandwidth from the graph. The algorithms for computing the constrained shortest paths can be used in many different circumstances, for instance, laying out virtual circuits in ATM networks, establishing wavelength- switching paths in fiber-optics networks, constructing label-switching paths. There are two schemes of implementing the QoS routing algorithms on routers. The first scheme is to implement them as on-line algorithms that process the routing requests as they arrive. In practice, on-line algorithms are not always desired. When the request arrival rate is high 1 To solve this problem, the second scheme is to extend a link-state protocol and periodically pre-compute the cheapest delay-constrained paths for all destinations, for instance, for traffic with an end-to-end delay requirement. The computed paths are cached for the duration before the next computation. This approach provides support for both constrained unicast and constrained multicast. The computation load on a router is independent of the request arrival rate. Moreover, many algorithms, including those we will propose shortly, have the same time complexity for computing constrained shortest paths to all destinations or to a single destination. This paper studies the second scheme.

2.2 Problem statement:

Shortest path computation is done with a single constraint, which is either based on cost or delay which causes an inefficient result. These results are approximated by ceiling and floor algorithms. Approximation by these techniques results in high error rate.


High Error rate.

Approximation Errors.

Difficulties in implementing Shortest path algorithms

2.3 Aim:

The aim of the project is to develop the Fast Computation of Constrained Shortest Paths


The first strategy is an exhaustive approach where approximation algorithms result in high error rate.

The second strategy is based on two constraints i.e.) delay and cost. These results are approximated by two new techniques such as randomized discretization and path delay discretization. These algorithms results in error rate reduction and results in increase of performance.

Minimized Error rate.

Efficient Approximation.

Easy implementation process.

3.1Analysis of existing work:

The first strategy is an exhaustive approach where approximation algorithms result in high error rate.

The second strategy is based on two constraints i.e.) delay and cost. These results are approximated by two new techniques such as randomized discretization and path delay discretization. These algorithms results in error rate reduction and results in increase of performance.

3.2 Modules:

Topology construction

Node information

Available path


Message transmission

Module Description:

Topology construction:

In this module we construct a topology with the following steps. The steps involve initializing the number of nodes, giving names to those nodes, initializing the port numbers for a particular node and provision of host name.

Node information:

In this module we provide the links for the initialized nodes. We also provide cost to the various links. We check there is no multiple links for same set of nodes. Cost specification is given to all nodes.


Available path:

In this module we get the total number of available paths for the particular topology. The steps involved in this process are, calculating the number of nodes, calculating the no of paths for a particular set of nodes and processing those paths when the particular set of nodes are chosen. This process also calculates the aggregate cost and delay for concurrent paths.


In this module we apply the discretization algorithms in order to approximate the aggregated delay and cost values for the paths specified.

The steps involved in this process are, getting the aggregate values of the path, applying discretization algorithms to the values, the discretization algorithms are round to ceiling, round to floor, randomized discretization and path delay discretization. This process happens only when a node decides to transmit.

Message transmission:

In this module the source node chooses the destination and the method of discretization for sending its message in the best path available. Once the client completes its message and sends the message, the client gets the knowledge about the available paths and it also gets the information about the best path and the details regarding the particular path.

4.1 Hardware Specification

Processor : Any Processor above 500 MHz.

Ram : 128Mb.

Hard Disk : 10 GB.

Compact Disk : 650 Mb.

Input device : Standard Keyboard and Mouse.

Output device : VGA and High Resolution Monitor.

4.2 Software Specification

Language : Java1.3

Front End Tool : Swing

Back End Tool : SQL Server2000

Operating System : Windows 98.


The data flow diagrams are very helpful in determining the flow of data in an application.


5.2 Module Diagram

Topology construction

Node information

Available path


Message transmission


The proposed techniques, randomized discretization and path delay discretization, to design fast algorithms for computing constrained shortest paths. While the previous approaches (RTF and RTC) build up the discretization error along a path, the new techniques either make the link errors to cancel out each other along the path or treat the path delay as a whole for discretization, which results in much smaller errors. The algorithms based on these techniques run much faster than the best existing algorithm that solves the eâ€"approximation.

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