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Approximation Algorithms for the Minimum Bends Traveling.. - Stein, Wagner (2000) (Correct)
....code in lines 9 through 13 achieves this. Thus we have shown: Theorem 4.1 Algorithm Find MBTSP, given an input to the Minimum Bends TSP problem, computes a tour which is a 2# 2 approximation, where # is the approximation bound for Set Cover. In general, the best set cover approximation is ln n [8, 13]. However, in the case when each set is of size no more than z, the approximation ratio is roughly ln z, and tighter bounds are known for small values of z[9] The maximum set size corresponds to the maximum number of collinear points and thus we have the following: Corollary 4.2 Given a set of ....
Dorit Hochbaum, editor. Approximation Algorithms. PWS, 1997.
Scheduling Algorithms - Karger, Stein, Wein (1997) (21 citations) (Correct)
....a target value T , and returns either no, asserting that no solution of value T exists, or returns a solution of value at most aeT . A polynomial time ae relaxed decision procedure can easily be converted into a ae approximation algorithm for the problem via binary search for the optimum T ; see [HS87, Hoc97] for more details. This simple idea is quite useful, as it essentially lets us pretend that we know the value T of an optimal solution to a problem. 5.1 Rounding a Fractional Assignment to Machines: RjjC max In this section we give a 2 relaxed decision procedure for RjjC max . Recall the linear ....
Dorit Hochbaum, editor. Approximation Algorithms. PWS, 1997.
Distributed Job Scheduling in Rings Perry Fizzano - Fizzano, Karger, Stein, Wein (Correct)
....problem, and L(I) the length of the shortest possible schedule for I. We call an algorithm A a ae approximation algorithm if it produces, on any instance I, a schedule of length no more than aeL(I) O(1) The worst case study of approximation algorithms has a long and rich history; see [15] for an extensive treatment. The major contribution of this paper is a distributed 4:22 approximation algorithm for scheduling jobs in a ring. Our algorithm has low control overhead, accounts for communication constraints and does not require global control. We note that, although our algorithm is ....
Dorit Hochbaum, editor. Approximation Algorithms. PWS, 1997. to appear.
Scheduling Algorithms - Karger, Stein, Wein (1997) (21 citations) (Correct)
....a target value T , and returns either no, asserting that no solution of value T exists, or returns a solution of value at most aeT . A polynomialtime ae relaxed decision procedure can easily be converted into a ae approximation algorithm for the problem via binary search for the optimum T ; see [HS87, Hoc97] for more details. This simple idea is quite useful, as it essentially lets us assume that we know the value T of an optimal solution to a problem. Note that this is a different use of the word relax than the term relaxation. 5.1 Rounding a Fractional Assignment to Machines: RjjC max In this ....
Dorit Hochbaum, editor. Approximation Algorithms. PWS, 1997.
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