Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The 3SUM conjecture has proven to be a valuable tool for proving conditional lor bounds on dynamic data structures and graph problems. This line of work was initiated by Pătrascu (STOC 2010) who reduced 3SUM to an offline SetDisjointness problem. Hover, the reduction introduced by Pătrascu suffers from several inefficiencies, making it difficult to obtain  tight  conditional lor bounds from the 3SUM conjecture.     address many of the deficiencies of Pătrascu's framework.  give new and efficient reductions from 3SUM to offline SetDisjointness and offline SetIntersection (the reporting version of SetDisjointness) which leads to polynomially higher lor bounds on several problems. Using our reductions,  are able to show the essential optimality of several algorithms, assuming the 3SUM conjecture.   • Chiba and Nishizeki's  O ( m α)-time algorithm (SICOMP 1985) for enumerating all triangles in a graph with arboricity/degeneracy α is essentially optimal, for any α.   • Bjorklund, Pagh, Williams, and Zwick's algorithm (ICALP 2014) for listing  t  triangles is essentially optimal (assuming the matrix multiplication exponent is ω = 2).   • Any static data structure for SetDisjointness that ansrs queries in constant time must spend Ω( N  2-- o (1) ) time in preprocessing, where  N  is the size of the set system.   These statements re unattainable via Pătrascu's reductions.    also introduce several new reductions from 3SUM to pattern matching problems and dynamic graph problems. Of particular interest are new conditional lor bounds for dynamic versions of Maximum Cardinality Matching, which introduce a new technique for obtaining amortized lor bounds.
['Tsvi Kopelowitz', 'Seth Pettie', 'Ely Porat']
I am writing a research paper on a idea Higher lower bounds from the 3SUM conjecture
[{"from": "human", "value": "I am writing a research paper on a idea Higher lower bounds from the 3SUM conjecture"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The 3SUM conjecture has proven to be a valuable tool for proving conditional lor bounds on dynamic data structures and graph problems. This line of work was initiated by P\u0103trascu (STOC 2010) who reduced 3SUM to an offline SetDisjointness problem. Hover, the reduction introduced by P\u0103trascu suffers from several inefficiencies, making it difficult to obtain  tight  conditional lor bounds from the 3SUM conjecture.     address many of the deficiencies of P\u0103trascu's framework.  give new and efficient reductions from 3SUM to offline SetDisjointness and offline SetIntersection (the reporting version of SetDisjointness) which leads to polynomially higher lor bounds on several problems. Using our reductions,  are able to show the essential optimality of several algorithms, assuming the 3SUM conjecture.   \u2022 Chiba and Nishizeki's  O ( m \u03b1)-time algorithm (SICOMP 1985) for enumerating all triangles in a graph with arboricity/degeneracy \u03b1 is essentially optimal, for any \u03b1.   \u2022 Bjorklund, Pagh, Williams, and Zwick's algorithm (ICALP 2014) for listing  t  triangles is essentially optimal (assuming the matrix multiplication exponent is \u03c9 = 2).   \u2022 Any static data structure for SetDisjointness that ansrs queries in constant time must spend \u03a9( N  2-- o (1) ) time in preprocessing, where  N  is the size of the set system.   These statements re unattainable via P\u0103trascu's reductions.    also introduce several new reductions from 3SUM to pattern matching problems and dynamic graph problems. Of particular interest are new conditional lor bounds for dynamic versions of Maximum Cardinality Matching, which introduce a new technique for obtaining amortized lor bounds."}]