Two lower bound arguments with "inaccessible" numbers

  • Martin Dietzfelbinger
  • Wolfgang Maass
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


We present lower bound arguments for two general computational models: linear decision trees (LDT's) and random access machines (RAM's). Both proofs use (besides combinatorial and geometrical arguments) the method of constructing "hard" instances (x1, ..., xn) of the considered problems, where the distances between some of the xi are chosen so large that from the point of view of a fixed computational model the larger numbers are "inaccessible" from the smaller ones. In §2 we further refine this technique: there we have to satisfy at the same time equalities between certain sums of input numbers in order to allow a "fooling argument". The mentioned techniques allow us to derive sharper lower bounds for a variety of computational problems, including KNAPSACK, SHORTEST PATH and ELEMENT DISTINCTNESS.


Edge Weight Knapsack Problem Linear Test Graph Problem Travel Salesperson Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Martin Dietzfelbinger
    • 1
  • Wolfgang Maass
    • 1
  1. 1.Department of MathematicsStatistics and Computer Science University of Illinois at ChicagoChicago

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