A unified approach to geometric problems using dual cone transformation:

References

• Avid , A. and Shamir , E. A. 1981 . Proc. 22nd FOCS symp. . A direct solution to range search and related problems for product regions . 1981 . pp. 123 – 26 .
   Google Scholar
• Bently , J. L. and Friedman , J. H. 1979 . Data structures for range searching . Comput. Surveys , II ( 4 ) 397 – 409 .
   Google Scholar
• Bently , J. L. and Maurer , H. A. 1980 . Efficient worst-case data structures for range searching . Acta Inform. , 13 ( 4 ) 155 – 168 .
   Google Scholar
• Chazelle , B. 1983 . Proc. 24th IEEE symp. Foundations ofComp. Sci . Filtering search: A new approach to query-answering . 1983 . pp. 122 – 132 .
   Google Scholar
• Dieudonnô , J. 1941 . Sur Théorémede Hahn-Banach . Rev. Sci. , 79 642 – 643 .
   Google Scholar
• Edelsbrunner H. Dynamic data structures for orthogonal intersection queries Techische Univ. of Graz 1980 Rep. 59
   Google Scholar
• Edelsbrunner , H. 1983 . A new approach to rectangle intersections, Part I . Internat. J. Comput. Math. , 13
   Google Scholar
• Edelsbrunner , H. and Maurer , H. A. 1981 . On the intersection of orthogonal objects . Inform. Process. Lett. , 13 ( 4-5 ) 177 – 180 .
   Web of Science ®Google Scholar
• Edelsbrunner , H. and Overmars , M. H. 1982 . On the equivalence of some rectangle problems . Inform. Process. Lett. , 14 ( 4-5 ) 124 – 127 .
   Google Scholar
• Fredman , M. L. 1981 . A lower bound on the complexity of orthogonal range queries . JACM , 28 ( 4 )
   Google Scholar
• Hille , E. and Phillips , R. 1957 . Functional Analysis and Semigroups . Am. Math. Soc. Colloq. Publ. , 31 ( 4 )
   Google Scholar
• Klee , V. L. 1951 . Convex sets in linear spaces . Duke Math. J. , 18 ( 2 ) 443 – 466 .
   Web of Science ®Google Scholar
• Lueker , G. 1978 . Proc. 19th IEEE symp. Foundations of Comp. Sci. . A data structure for orthogonal range queries . 1978 . pp. 28 – 34 .
   Google Scholar
• McCreight E. M Priority search trees 1981 Xerox PARC, Palo Alto, Report CSL-81-5
   Google Scholar
• Sandgren , L. 1954 . On Convex Cones . Math. Scand. , 2 19 – 28 .
   Google Scholar
• Six , H. W. and Wood , D. 1980 . The rectangle intersection problem revisited . BIT , 20 426 – 433 .
   Google Scholar
• Vashnaivi , V. K. 1982 . Computing point enclosures . IEEE Trans. Comp. , C-31 22 – 29 .
   Google Scholar
• Willard , D. E. 1985 . New data structures for orthogonal range queries . Siam. J. Comput. , 14 ( 1 ) 232 – 253 .
   Web of Science ®Google Scholar