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Algorithmica

, Volume 33, Issue 4, pp 494–510 | Cite as

Optimal Solutions for the Temporal Precedence Problem

  •  Brodal
  •  Makris
  •  Sioutas
  •  Tsakalidis
  •  Tsichlas

Abstract. In this paper we refer to the Temporal Precedence Problem on Pure Pointer Machines . This problem asks for the design of a data structure, maintaining a set of stored elements and supporting the following two operations: insert and precedes . The operation insert (a) introduces a new element a in the structure, while the operation precedes (a,b) returns true iff element a was inserted before element b temporally. In [11] a solution was provided to the problem with worst-case time complexity O (log log n ) per operation and O(n log log n) space, where n is the number of elements inserted. It was also demonstrated that the precedes operation has a lower bound of Ω (log log n ) for the Pure Pointer Machine model of computation. In this paper we present two simple solutions with linear space and worst-case constant insertion time. In addition, we describe two algorithms that can handle the precedes (a,b) operation in O (log log d ) time, where d is the temporal distance between the elements a and b .

Key words. Algorithms, Dynamic data structures, Computational complexity. 

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Copyright information

© Springer-Verlag New York Inc. 2002

Authors and Affiliations

  •  Brodal
    • 1
  •  Makris
    • 2
  •  Sioutas
    • 2
  •  Tsakalidis
    • 2
  •  Tsichlas
    • 2
  1. 1.BRICS (Basic Research in Computer Science), Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000 Arhus C, Denmark.DK
  2. 2.Department of Computer Engineering & Informatics, University of Patras, 26500 Patras, Greece, and Computer Technology Institute (CTI), P.O. Box 1192, 26110 Patras, Greece.GR

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