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2answers
1k views

Greedy approach to 0-1 Knapsack problem in specific instances

The 0-1 knapsack problem is known to be NP-complete, and the greedy approach by Dantzig (based on choosing on the basis of density or value/weight) can be shown to be suboptimal using counterexamples. ...
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2answers
639 views

Approximate Algorithms for Poisson's Equation (PDE)

Are there some approximate or randomised algorithms to numerically solve Poisson's Equation in Partial Differential Equations.(http://en.wikipedia.org/wiki/Poisson%27s_equation). The best algorithms I ...
3
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0answers
192 views

Algorithm for testing satisfiable fraction of linear equations mod 2

Hello Let $F_{n,p}$ be a random process which generates a system of linear equations over $F_2$. The variables are $\{x_1, ..., x_n\}$ and for each of the $ \binom{n}{2}$ $i,j$ pairs, the equation ...
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2answers
307 views

Approximation of conformal mapping as a sum of elementary conformal mappings

Hi, I would like to approximate any 2d conformal mapping, as a sum of elementary conformal mappings. So I would have some basis, a conformal mapping with some parameters, and by adding several ones ...
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3answers
862 views

Approximating e with 2s and 3s

How can I generate a series of 2s and 3s such that the average of the generated values (so far) is as close to e as possible? For example: ...
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1answer
3k views

HOW TO Generate Equation of a Curve Given (x,y) pairs - algorithm? [closed]

Hi, How can I generate the equation of a curve that matches all arbitrarily given (x,y) pairs? I would like a polynomial of nth degree, where n does not matter, as long as the curve passes thru all ...
4
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1answer
582 views

Hypergraph Chromatic Number vs Degree, Clique-Size

For a hypergraph let $\chi$ be the least number of colours needed to colour the vertices, so that in each edge, each colour is used at most once (i.e., the strong chromatic number). Let $\Delta$ be ...
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2answers
959 views

Analyzing Weighted Set-Cover variant

A standard greedy algorithm for solving the weighted set-cover problem can be proven to be a $\log(n)$ approximation. I have a variant of weighted set cover, and I came up with a greedy algorithm for ...