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Introduction to Algorithms, Second Edition
TLDR
The complexity class P is formally defined as the set of concrete decision problems that are polynomial-time solvable, and encodings are used to map abstract problems to concrete problems.
Introduction to Algorithms, third edition
TLDR
Pseudo-code explanation of the algorithms coupled with proof of their accuracy makes this book a great resource on the basic tools used to analyze the performance of algorithms.
A new approach to the minimum cut problem
TLDR
A randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability with a significant improvement over the previous time bounds based on maximum flows.
Approximation techniques for average completion time scheduling
TLDR
It is shown that a preemptive one-machine relaxation is a powerful tool for designing parallel machine scheduling algorithms that simultaneously produce good approximations and have small running times, and a general theorem relating the value of one- machine relaxations to that of the schedules obtained for the original m-machine problems is proved.
Approximation schemes for minimizing average weighted completion time with release dates
TLDR
This work presents the first known polynomial time approximation schemes for several variants of the problem of scheduling n jobs with release dates on m machines so as to minimize their average weighted completion time.
Optimal Time-Critical Scheduling via Resource Augmentation
TLDR
This work establishes that several well-known on-line algorithms, that have poor performance from an absolute worst-case perspective, are optimal for the problems in question when allowed moderately more resources.
Minimizing average completion time in the presence of release dates
TLDR
This paper gives the first constant-factor approximation algorithms for several variants of the single and parallel machine models and generalizes to the minimization of averageweighted completion time as well.
Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs
TLDR
These techniques lead to the first approximation algorithm and obtain an approximation ratio that matches, to within logarithmic factors, the $O(\sqrt{|E|})$ approximation ratio for the simple edge-disjoint path problem.
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