Showing papers on "Greedy algorithm published in 1978"

Accelerated greedy algorithms for maximizing submodular set functions

Abstract: Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E maximizing f over P(E). Many combinatorial optimization problems can be formulated in these terms. Here, a family of approximate solution methods is studied : the greedy algorithms.

Computer Algorithms: Introduction to Design and Analysis

Abstract: From the Publisher: This edition features an increased emphasis on algorithm design techniques such as divide-and-conquer and greedy algorithms, along with the addition of new topics and exercises. It continues the tradition of solid mathematical analysis and clear writing style: emphasizes the development of algorithms through a step-by-step process rather than by merely presenting the end result; stresses the importance of the algorithm analysis process - continuously re-evaluating, modifying, and perhaps rejecting algorithms until a satisfactory solution is attained; provides extensive treatment of recursion with a clear, student-friendly review of how it works and why it is a valuable programming technique; uses a Java-like pseudocode; and includes an appendix with java examples.

Approximation Algorithms for Some Routing Problems

Abstract: Several polynomial time approximation algorithms for some $NP$-complete routing problems are presented, and the worst-case ratios of the cost of the obtained route to that of an optimal are determined. A mixed-strategy heuristic with a bound of 9/5 is presented for the stacker-crane problem (a modified traveling salesman problem). A tour-splitting heuristic is given for k-person variants of the traveling salesman problem, the Chinese postman problem, and the stacker-crane problem, for which a minimax solution is sought. This heuristic has a bound of $e + 1 - 1/k$, where e is the bound for the corresponding 1-person algorithm.

An Analysis of the Greedy Heuristic for Independence Systems

Abstract: The worst case behaviour of the greedy heuristic for independence systems is analyzed by deriving lower bounds for the ratio of the greedy solution value to the optimal value. For two special independence systems, this ratio can be bounded by 1/2, for two other independence systems, it converges with increasing problem size to zero. The main theorem states that for every independence system ( E , F ) the ratio is bounded by I/k, k such that ( E , F ) can be represented as the intersection of k matroids.

K-greedy algorithms for independence systems

Abstract: Recently inJenkyns [1976] andKorte/Hausmann [1978] a tight worst-case bound for the well-known greedy heuristic for general independence systems has been deduced. Here some modifications of the greedy heuristic are investigated which allow to enlarge the current independent set by more than one element. It is shown that in spite of the additional enumeration incorporated in these heuristics they can behave worse than the usual greedy heuristic for some problem instances. For one of those modifications the same worst-case bound as mentioned above — but no better one — has been proved again. These results underline the predominant role of the usual greedy heuristic for general independence systems.

The Held—Karp algorithm and degree-constrained minimum 1-trees

Abstract: In this note we propose to find a degree-constrained minimum 1-tree in the Held—Karp algorithm [5, 6] for the symmetric traveling-salesman problem, and show that it is reduced to finding a minimum common basis of two matroids.

Maximization problems on graphs with edge weights chosen from a normal distribution

Abstract: Author(s): Lueker, George S. | Abstract: We consider optimization problems on complete graphs with edge weights chosen from identical but independent normal distributions. We show some very general techniques for obtaining upper and lower bounds on the asymptotic behavior of these problems. Often, but not always, these bounds are equal, enabling us to state the asymptotic behavior of the maximum. Problems in which the bounds are tight include finding the optimum traveling salesman tour, finding a minimum cost spanning tree, and finding a heaviest clique on k vertices. We then discuss some greedy heuristic algorithms for these problems.

Maximization problems on graphs with edge weights chosen from a normal distribution (Extended Abstract)

Abstract: we consider optimization problems on complete graphs with edge weights chosen from identical but independent normal distributions. We show some very general techniques for obtaining upper and lower bounds on the asymptotic behavior of these problems. Often, but not always, these bounds are equal, enabling us to state the asymptotic behavior of the maximum. Problems in which the bounds are tight include finding the optimum traveling salesman tour, finding a minimum cost spanning tree, and finding a heaviest clique on k vertices. We then discuss some greedy heuristic algorithms for these problems.

Optimization techniques : proceedings of the 8th IFIP Conference on Optimization Techniques, Würzburg, September, 5-9, 1977

Abstract: Semi-infinite programming: Conditions of optimality and applications.- On equiwellset minimum problems.- Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems.- An underrelaxed gauss-newton method for equality constrained nonlinear least squares problems.- A modification of Robinson's algorithm for general nonlinear programming problems requiring only approximate solutions of subproblems with linear equality constraints.- On a minimization problem in structural mechanics.- Non-linear least squares inversion of an integral equation using free-knot cubic splines.- On the convergence of the modified tui algorithm for minimizing a concave function on a bounded convex polyhedron.- A class of algorithms for the determination of a solution of a system of nonlinear equations.- Stochastic linear programs with random data having stable distributions.- Methods of feasible directions with increased gradient memory.- The continuous method of steepest descent and its discretizations.- Convergence rate results for a penalty function method.- A combined variable metric - Conjugate Gradient algorithm for a class of large scale unconstrained minimization problems.- Simplex method for dynamic linear program solution.- An adaptive precision method for the numerical solution of constrained optimization problems applied to a time-optimal heating process.- Generalized inverses and a new stable secant type minimization algorithm.- A conjugate directions method and its application.- The development of an efficient optimal control package.- An accuracy selection algorithm for the modified gradient projection method in minimax problems.- Single-iterative saddle-point algorithms for solving constrained optimization problems via augmented Lagrangians.- Improved lower bounds to 0/1 problems via lagrangean relaxation.- A unified approach to reshipment, overshipment and post-optimization problems.- Solving an integer programming problem.- Worst-case analysis for a class of combinatorial optimization algorithms.- An improved method of successive optima for the assignment problem.- Accelerated greedy algorithms for maximizing submodular set functions.- Resource allocation in a set of networks under multiple objectives.- An algorithm for solving the generalized transportation problem.- An efficient algorithm for solving a stochastic, integer programming problem arising in radio navigation.- Using pseudoboolean programming in decomposition method.- Solving the general project scheduling problem with multiple constrained resources by mathematical programming.- Threshold methods for boolean optimization problems with separable objectives.- Comparison of some educational planning models.- Mathematical programming in health-care planning.- A model of housing developing costs related to location.- An optimum surveillance and control system for synchronized traffic signals.- Regional classification problem and weaver's method.- A mathematical model for decision making in public service planning.- Optimal control of regional economic growth.- System modeling for interconnected dynamic economy and the decentralized optimal control.- Economic consequences of a change in demographic patterns: A linear programming model.- The multiple covering problem and its application to the dimensioning of a large scale seismic network.- A remark on econometric modelling, optimization and decision making.- Formulation and solution of the sequencing problem with parallel machines.- Stochastic model of resource allocation to R & D activities under cost value uncertainty.- Scheduling of trains - An optimization approach.- Optimal portfolios where proceeds are a function of the current asset price.- An algorithm for optimal sequencing of aircraft in the near terminal area.- A mathematical model of traffic in communication networks.- Partitioning a computer network into subnetworks and allocation of distributed data bases.- Effective file allocation method onto disc devices.- Optimal file allocation problem and relational distributed data bases.- General purpose nonlinear programming package.