We describe a very simple and efficient new algorithm for the approximation of complex numbers by algebraic integers in Z[e 2i=8 ] whose coeffcients with respect to the usual basis are bounded in absolute value by a given integer M . Its main idea is the use of a novel signature technique

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We present a linear time approximation algorithm with a performance ratio of 1/2 for nding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis [7].

this paper will show how to implement this algorithm in O(N log N) time

We present a simple 4-approximation algorithm for the extensively-studied Capacitated Minimum Spanning Tree problem. The approximation ratio of our algorithm matches the current best ratio of 4, due to Altinkemer and Gavish. Our algorithm is simpler, and easier to analyze when compared

with attention to interference-free channel assignment or scheduling. Then we propose some simple approximation algorithms and/or PTASs (polynomial time approximation scheme) to approximate several classical graph problems such as maximum independent set, minimum vertex cover and minimum vertex coloring

of all half-spaces containing A. The first idea to approximate the convex hull, inspired by k-DOP bounding volumes [1], is to restrict the set of intersected halfspaces. In particular, we confine ourselves to k half-spaces defined as follows. Let angle α = 2π k. We can partition the plane to sectors

simple and efficient algorithm for determining an approximate market equilibrium. Our algorithm finds an �-approximate solution in O�n/���B��G�� � time, where n = �B � + �G�. The running time can be further improved to O�n/��m + �B � log �B�� � where m is the number of pairs �i � j � such that buyer i

. We describe a very simple and efficient new algorithm for the approximation of complex numbers by algebraic integers in Z[e 2ßi=8 ] whose coefficients with respect to the usual basis are bounded in absolute value by a given integer M . Its main idea is the use of a novel signature technique

and the positions of all nodes are available. On one hand, it admits a polynomial-time approximation scheme (PTAS). In other words, for any fixed