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» Approximate counting in bounded arithmetic
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STOC
2005
ACM
167views Algorithms» more  STOC 2005»
14 years 7 months ago
Approximately counting integral flows and cell-bounded contingency tables
We consider the problem of approximately counting integral flows in a network. We show that there is an fpras based on volume estimation if all capacities are sufficiently large, ...
Mary Cryan, Martin E. Dyer, Dana Randall
DAGSTUHL
2008
13 years 9 months ago
Complete Interval Arithmetic and its Implementation
: Let IIR be the set of closed and bounded intervals of real numbers. Arithmetic in IIR can be defined via the power set IPIR of real numbers. If divisors containing zero are exclu...
Ulrich W. Kulisch
SODA
2010
ACM
202views Algorithms» more  SODA 2010»
14 years 4 months ago
Counting Inversions, Offline Orthogonal Range Counting, and Related Problems
We give an O(n lg n)-time algorithm for counting the number of inversions in a permutation on n elements. This improves a long-standing previous bound of O(n lg n/ lg lg n) that ...
Timothy M. Chan, Mihai Patrascu
JC
2008
77views more  JC 2008»
13 years 7 months ago
A numerical algorithm for zero counting, I: Complexity and accuracy
We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(log(nD(f))) iterations (grid refinements) where n is...
Felipe Cucker, Teresa Krick, Gregorio Malajovich, ...
COMPGEOM
2004
ACM
14 years 26 days ago
Deterministic sampling and range counting in geometric data streams
We present memory-efficient deterministic algorithms for constructing -nets and -approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic...
Amitabha Bagchi, Amitabh Chaudhary, David Eppstein...