Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: One of the fundamental trade-offs in compact routing schemes is beten the  space  used to store the routing table on each node and the  stretch  factor of the routing scheme -- the ratio beten the cost of the route induced by the scheme and the cost of a minimum cost path beten the same pair. Using a distributed Kolmogorov Complexity argument,  give a lor bound for the name-independent model that applies even to single-source schemes and does not require a girth conjecture. For any integer  k  ≥ 1  prove that any routing scheme for networks with arbitrary ights and arbitrary node names (even a single-source routing scheme) with maximum stretch strictly less than 2 k  + 1 requires Ω(( n  log  n ) 1/ k  )-bit routing tables.  extend our results to lor bound the average-stretch, showing that for any integer  k  ≥ 1 any name-independent routing scheme with ( n /(9 k )) 1/ k  -bit routing tables has average-stretch of at least  k /4 + 7/8. This result is in sharp contrast to recent results on the average-stretch of labeled routing schemes.
['Ittai Abraham', 'Cyril Gavoille', 'Dahlia Malkhi']
I am writing a research paper on a idea On space-stretch trade-offs: lower bounds
[{"from": "human", "value": "I am writing a research paper on a idea On space-stretch trade-offs: lower bounds"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: One of the fundamental trade-offs in compact routing schemes is beten the  space  used to store the routing table on each node and the  stretch  factor of the routing scheme -- the ratio beten the cost of the route induced by the scheme and the cost of a minimum cost path beten the same pair. Using a distributed Kolmogorov Complexity argument,  give a lor bound for the name-independent model that applies even to single-source schemes and does not require a girth conjecture. For any integer  k  \u2265 1  prove that any routing scheme for networks with arbitrary ights and arbitrary node names (even a single-source routing scheme) with maximum stretch strictly less than 2 k  + 1 requires \u03a9(( n  log  n ) 1/ k  )-bit routing tables.  extend our results to lor bound the average-stretch, showing that for any integer  k  \u2265 1 any name-independent routing scheme with ( n /(9 k )) 1/ k  -bit routing tables has average-stretch of at least  k /4 + 7/8. This result is in sharp contrast to recent results on the average-stretch of labeled routing schemes."}]