Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider two new variants of online integer programs that are duals. In the packing problem  are given a set of items and a collection of knapsack constraints over these items that are revealed over time in an online fashion. Upon arrival of a constraint  may need to remove several items (irrevocably) so as to maintain feasibility of the solution. Hence, the set of packed items becomes smaller over time. The goal is to maximize the number, or value, of packed items. The problem originates from a bu↵er-overflow model in communication networks, where items represent information units broken into multiple packets. The other problem considered is online covering: There is a universe to be covered. Sets arrive online, and  must decide for each set whether  add it to the cover or give it up. The cost of a solution is the total cost of sets taken, plus a penalty for each uncovered element. The number of sets in the solution grows over time, but its cost goes down. This problem is motivated by team formation, where the universe consists of skills, and sets represent candidates  may hire. The packing problem was introduced in [8] for the special case where the matrix is binary; in this paper  extend the solution to general matrices with non-negative integer entries. The covering problem is introduced in this paper;  present matching upper and lor bounds on its competitive ratio.
['Pierre Fraigniaud', 'Magnús M. Halldórsson', 'Boaz Patt-Shamir', 'Dror Rawitz', 'Adi Rosén']
I am writing a research paper on a idea Shrinking Maxima, Decreasing Costs: New Online Packing and Covering Problems.
[{"from": "human", "value": "I am writing a research paper on a idea Shrinking Maxima, Decreasing Costs: New Online Packing and Covering Problems."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider two new variants of online integer programs that are duals. In the packing problem  are given a set of items and a collection of knapsack constraints over these items that are revealed over time in an online fashion. Upon arrival of a constraint  may need to remove several items (irrevocably) so as to maintain feasibility of the solution. Hence, the set of packed items becomes smaller over time. The goal is to maximize the number, or value, of packed items. The problem originates from a bu\u21b5er-overflow model in communication networks, where items represent information units broken into multiple packets. The other problem considered is online covering: There is a universe to be covered. Sets arrive online, and  must decide for each set whether  add it to the cover or give it up. The cost of a solution is the total cost of sets taken, plus a penalty for each uncovered element. The number of sets in the solution grows over time, but its cost goes down. This problem is motivated by team formation, where the universe consists of skills, and sets represent candidates  may hire. The packing problem was introduced in [8] for the special case where the matrix is binary; in this paper  extend the solution to general matrices with non-negative integer entries. The covering problem is introduced in this paper;  present matching upper and lor bounds on its competitive ratio."}]