Remembering Leo Khachiyan

Scientific contributions of Leo Khachiyan (a short overview)

OnApril 29, 2005, LeoKhachiyan passed awaywith tragic suddenness in themiddle of his scientific career. He became famous for his polynomial time algorithm for linear programming (LP)[L. Khachiyan, A polynomial algorithm in linear programming, Soviet Math. Doklady 20 (1) (1979) 191–194; L. Khachiyan, Polynomial algorithms for linear programming, USSR Comp. Math. and Math. Phys. 20 (2) (1980) 51–...

Remembering LEO

It is now more than 60 years since the world’s first business use of a computer, the valuation of bakery output, was rolled-out the LEO I computer at Cadby Hall in London, the headquarters of the food production and catering company J. Lyons and Company. LEO I had been designed and built as a computer to be used for business data processing by a team of engineers recruited by Lyons, with a basi...

My Memories of Leonid Khachiyan and a Personal Tribute for His Contributions in Linear Programming

Approximate Minimum - Cost Multicommodity Flows in ~ O ( " � 2 Knm ) Time

We show that an "-approximate solution of the cost-constrained K-commodity ow problem on an N-nodeM-arc network G can be computed by sequentially solving O K(" 2 + logK) logM log(" 1 K) single-commodity minimum-cost ow problems on the same network. In particular, an approximate minimumcost multicommodity ow can be computed in ~ O(" 2 KNM) running time, where the notation ~ O( ) means \up to log...

حفاظ‌های چندلایه در مدار LEO

LEO orbit space radiations in which the protons has the main contribution, have survived devastating effects on electronic components. The damage caused by ionizing protons on the satellite electrical components in the circuit LEO moves was reviewed. By studying the LEO orbit by Shieldose software, the worst-case scenario was evaluated for a satellite. Considering the electronic components base...