3,359 research outputs found
Threesomes, Degenerates, and Love Triangles
The 3SUM problem is to decide, given a set of real numbers, whether any
three sum to zero. It is widely conjectured that a trivial -time
algorithm is optimal and over the years the consequences of this conjecture
have been revealed. This 3SUM conjecture implies lower bounds on
numerous problems in computational geometry and a variant of the conjecture
implies strong lower bounds on triangle enumeration, dynamic graph algorithms,
and string matching data structures.
In this paper we refute the 3SUM conjecture. We prove that the decision tree
complexity of 3SUM is and give two subquadratic 3SUM
algorithms, a deterministic one running in
time and a randomized one running in time with
high probability. Our results lead directly to improved bounds for -variate
linear degeneracy testing for all odd . The problem is to decide, given
a linear function and a set , whether . We show the
decision tree complexity of this problem is .
Finally, we give a subcubic algorithm for a generalization of the
-product over real-valued matrices and apply it to the problem of
finding zero-weight triangles in weighted graphs. We give a
depth- decision tree for this problem, as well as an
algorithm running in time
Parallel multiplication and powering of polynomials
AbstractThis paper examines the most efficient known serial and parallel algorithms for multiplying and powering polynomials. For sparse polynomials the Simp algorithm multiplies using a simple divide and conquer approach, and the NOMC algorithm computes powers using a multinomial expansion. For dense polynomials the FFT multiplies and powers by evaluating polynomials at a set of points, performing pointwise multiplication or powering, and interpolating a polynomial through the results. Practical issues of applying these algorithms in algebraic manipulation systems are discussed
Improvements in understanding and performance of multi-objective differential evolution (多目的差分進化における理解の深化と性能向上)
信州大学(Shinshu university)博士(工学)ThesisDROZDIK MARTIN. Improvements in understanding and performance of multi-objective differential evolution (多目的差分進化における理解の深化と性能向上). 信州大学, 2015, 博士論文. 博士(工学), 甲第630号, 平成27年3月20日授与.doctoral thesi
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