On extremal behaviors of Murty's least index method

@article{Fukuda1994OnEB,
  title={On extremal behaviors of Murty's least index method},
  author={Komei Fukuda and Makoto Namiki},
  journal={Mathematical Programming},
  year={1994},
  volume={64},
  pages={365-370},
  url={https://api.semanticscholar.org/CorpusID:21476636}
}
It is shown that the expected number of steps for solving Murty's exponential example with a random permutation of variable indices is exactly equal ton, wheren is the size of the input square matrix.
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14 Citations
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14 Citations

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This thesis determines bounds on sizes of USO classes arising from pivoting in P-LCPs and concludes that P-USOs contain much more combinatorial structure, which is needed to prove polynomial runtime of an existing pivot rule or to devise superior rules for simple principal pivoting algorithms.

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5 References

A short proof of finiteness of Murty's principal pivoting algorithm

We give a short proof of the finiteness of Murty's principal pivoting algorithm for solving the linear complementarity problemy = Mz + q, y T z = 0,y ≥ 0,z ≥ 0 withP-matrixM.

An exponential example for Terlaky's pivoting rule for the criss-cross simplex method

It is shown that the required number of iterations may be exponential in the number of variables and constraints of the problem.

Some generalizations of the criss-cross method for the linear complementarity problem of oriented matroids

Here some generalizations of Terlaky's finite criss-cross method are presented for oriented matroid quadratic programming and two special cases (oriented matroid linear programming and the definite case) are discussed.

LINEAR COMPLEMENTARITY AND ORIENTED MATROIDS

A combinatorial abstraction of the linear complementarity theory in the setting of oriented matroids was first considered by M.J. Todd. In this paper, we take a fresh look at this abstraction, and…

Computational complexity of complementary pivot methods

The class of orthants in R n contains 2n orthants. A straight line L in R n is said to cut across an orthant C of R n if L has a nonempty intersection with the interior of C. It is well known that…