Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Two mobile agents, starting from different nodes of a network at possibly different times, have to meet at the same node. This problem is known as rendezvous. Agents move in synchronous rounds. Each agent has a distinct integer label from the set $$\{1,\ldots ,L\}$${1,?,L}. Two main efficiency measures of rendezvous are its time (the number of rounds until the meeting) and its cost (the total number of edge traversals).  investigate tradeoffs beten these two measures. A natural benchmark for both time and cost of rendezvous in a network is the number of edge traversals needed for visiting all nodes of the network, called the exploration time. Hence  express the time and cost of rendezvous as functions of an upper bound E on the time of exploration (where E and a corresponding exploration procedure are known to both agents) and of the size L of the label space.  present two natural rendezvous algorithms. Algorithm Cheap has cost O(E) (and, in fact, a version of this algorithm for the model where the agents start simultaneously has cost exactly E) and time O(EL). Algorithm Fast has both time and cost $$O(E\log L)$$O(ElogL). Our main contributions are lor bounds showing that, perhaps surprisingly, these two algorithms capture the tradeoffs beten time and cost of rendezvous almost tightly.  show that any deterministic rendezvous algorithm of cost asymptotically E (i.e., of cost $$E+o(E)$$E+o(E)) must have time $$\varOmega (EL)$$Ω(EL). On the other hand,  show that any deterministic rendezvous algorithm with time complexity $$O(E\log L)$$O(ElogL) must have cost $$\varOmega (E\log L)$$Ω(ElogL).
['Avery Miller', 'Andrzej Pelc']
I am writing a research paper on a idea Time versus cost tradeoffs for deterministic rendezvous in networks
[{"from": "human", "value": "I am writing a research paper on a idea Time versus cost tradeoffs for deterministic rendezvous in networks"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Two mobile agents, starting from different nodes of a network at possibly different times, have to meet at the same node. This problem is known as rendezvous. Agents move in synchronous rounds. Each agent has a distinct integer label from the set $$\\{1,\\ldots ,L\\}$${1,?,L}. Two main efficiency measures of rendezvous are its time (the number of rounds until the meeting) and its cost (the total number of edge traversals).  investigate tradeoffs beten these two measures. A natural benchmark for both time and cost of rendezvous in a network is the number of edge traversals needed for visiting all nodes of the network, called the exploration time. Hence  express the time and cost of rendezvous as functions of an upper bound E on the time of exploration (where E and a corresponding exploration procedure are known to both agents) and of the size L of the label space.  present two natural rendezvous algorithms. Algorithm Cheap has cost O(E) (and, in fact, a version of this algorithm for the model where the agents start simultaneously has cost exactly E) and time O(EL). Algorithm Fast has both time and cost $$O(E\\log L)$$O(ElogL). Our main contributions are lor bounds showing that, perhaps surprisingly, these two algorithms capture the tradeoffs beten time and cost of rendezvous almost tightly.  show that any deterministic rendezvous algorithm of cost asymptotically E (i.e., of cost $$E+o(E)$$E+o(E)) must have time $$\\varOmega (EL)$$\u03a9(EL). On the other hand,  show that any deterministic rendezvous algorithm with time complexity $$O(E\\log L)$$O(ElogL) must have cost $$\\varOmega (E\\log L)$$\u03a9(ElogL)."}]