Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A fundamental problem in quality-of-service (QoS) routing is the multiconstrained path (MCP) problem, where one seeks a source-destination path satisfying K > 2 additive QoS constraints in a network with K additive QoS parameters. The MCP problem is known to be NP-complete. One popular approach is to use the shortest path with respect to a single edge ighting function as an approximate solution to MCP. In a pioneering work, Jaffe shod that the shortest path with respect to a scaled 1-norm of the K edge ights is a 2-approximation to MCP in the sense that the sum of the larger of the path ight and its corresponding constraint is within a factor of 2 from minimum. In a recent paper, Xue et al. shod that the shortest path with respect to a scaled oc-norm of the K edge ights is a K-approximation to MCP, in the sense that the largest ratio of the path ight over its corresponding constraint is within a factor of K from minimum. ,  study the relationship beten these two optimization criteria and present a class of provably good approximation algorithms to MCP.  first prove that a good approximation according to the second optimization criterion is also a good approximation according to the first optimization criterion, but not vice versa.  then present a class of very simple K-approximation algorithms according to the second optimization criterion, based on the computation of a shortest path with respect to a single edge ighting function
['Guoliang Xue', 'S.K. Makki']
I am writing a research paper on a idea Multiconstrained QoS Routing: A Norm Approach
[{"from": "human", "value": "I am writing a research paper on a idea Multiconstrained QoS Routing: A Norm Approach"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A fundamental problem in quality-of-service (QoS) routing is the multiconstrained path (MCP) problem, where one seeks a source-destination path satisfying K > 2 additive QoS constraints in a network with K additive QoS parameters. The MCP problem is known to be NP-complete. One popular approach is to use the shortest path with respect to a single edge ighting function as an approximate solution to MCP. In a pioneering work, Jaffe shod that the shortest path with respect to a scaled 1-norm of the K edge ights is a 2-approximation to MCP in the sense that the sum of the larger of the path ight and its corresponding constraint is within a factor of 2 from minimum. In a recent paper, Xue et al. shod that the shortest path with respect to a scaled oc-norm of the K edge ights is a K-approximation to MCP, in the sense that the largest ratio of the path ight over its corresponding constraint is within a factor of K from minimum. ,  study the relationship beten these two optimization criteria and present a class of provably good approximation algorithms to MCP.  first prove that a good approximation according to the second optimization criterion is also a good approximation according to the first optimization criterion, but not vice versa.  then present a class of very simple K-approximation algorithms according to the second optimization criterion, based on the computation of a shortest path with respect to a single edge ighting function"}]