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Showing papers on "Greedy algorithm published in 1979"


Journal ArticleDOI
TL;DR: It turns out that the ratio between the two grows at most logarithmically in the largest column sum of A when all the components of cT are the same, which reduces to a theorem established previously by Johnson and Lovasz.
Abstract: Let A be a binary matrix of size m × n, let cT be a positive row vector of length n and let e be the column vector, all of whose m components are ones. The set-covering problem is to minimize cTx subject to Ax ≥ e and x binary. We compare the value of the objective function at a feasible solution found by a simple greedy heuristic to the true optimum. It turns out that the ratio between the two grows at most logarithmically in the largest column sum of A. When all the components of cT are the same, our result reduces to a theorem established previously by Johnson and Lovasz.

2,645 citations


Proceedings ArticleDOI
01 Jan 1979
TL;DR: This paper presents a conceptionally simple algorithm which decides the type of a query when the number of domains in common between two relations may exceed one and runs in 0(max(e,e'), O(e) space complexity.
Abstract: The aim is to process distributed queries ef ficiently. The cost of communications between sites is dominant in processing such queries. It is assumed that the amount of data transferred determines the transmission cost to a large extent. Thus, it is desirable to minimize the amount of transmitted data. Bernstein-and Chiu [2] classified queries into two types: tree and cyclic queries. They defined an operation called semi-join which requires minimal transfer of data between sites. Then they showed that tree queries can always be answered by semi-joins but cyclic queries may not. An algorithm to decide whether a query is cyclic or not was presented in their paper. Their algorithm works when the number of domains in common between any two relations is no more than one. The aim of this paper is to generalize their algorithm. Specifically, we present a conceptionally simple algorithm which decides the type of a query when the number of domains in common between two relations may exceed one. An implementation of the algorithm is outlined. The algorithm runs in 0(max(e,e')) time and O(e) space complexity where e and e' are the number of edges in the transitive closure of the join graph and the query graph respectively.

119 citations


Journal ArticleDOI
TL;DR: A direct dual method is given, consisting of several phases (each of which appears essential for some data), to resolve a strong relaxed form of the mixed plant location problem with additional constraints over the integer variables.
Abstract: The mixed plant location problem (mixed in the sense of allowing capacitated as well as uncapacitated plants) is a difficult and important mixed integer problem. We give a direct dual method, consisting of several phases (each of which appears essential for some data), to resolve a strong relaxed form of the problem with additional constraints over the integer variables (user specified, or derived from the data themselves). When all features of the algorithm are employed, there appears to be no difficulty with problems of 100 plants, even in an inefficient computer implementation. The primal solutions which we derive from the orthogonality conditions and a simple greedy heuristic are almost always much better than those we obtain from a standard relaxed problem in the Lagrangean sense. With an enumeration code in an efficient implementation we would expect to be capable of resolving very large problems (of perhaps up to 500 or 1000 plants) to within practically well acceptable tolerances.

101 citations


Journal ArticleDOI
TL;DR: Those independence systems on finite partially ordered sets are characterized for which the greedy algorithm always works.

41 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of a firm which must lease warehouse space over a finite planning horizon is considered, and the dual to the linear program is shown to be equivalent to a network flow problem which can be solved via a greedy algorithm, and admits a simple primal variable recovery procedure.
Abstract: In this paper we consider the problem of a firm which must lease warehouse space over a finite planning horizon. Demand for space in each time period is a random variable with known density function. The firm contracts for warehouse space for each time period at the beginning of the planning horizon via a primary contract. If demand exceeds space in any period, additional space can be obtained via a secondary contract. The leasing problem is shown to be equivalent to a linear programming problem under reasonable assumptions. The dual to the linear program is shown to be equivalent to a network flow problem which can be solved via a greedy algorithm, and admits a rather simple primal variable recovery procedure. Computational evidence indicates that dual problems with some 200,000 arcs can be solved efficiently.

30 citations


Journal ArticleDOI
T. A. Jenkyns1
01 Dec 1979-Networks
TL;DR: It is shown that G*-W* may be as large as f(n,M,W*) where n is the number of vertices and M is the maximum edge-weight.
Abstract: The Travelling Salesman's Problem is to find a Hamilton path (or circuit) which has minimum total weight W*, in a graph (or digraph) with a non-negative weight on each edge. The Greedy Travelling Salesman's Problem is “How much larger than W* can the total weight G* of the solution obtained by the Greedy Algorithm be?”. Using the theory of independence systems, it is shown that G*-W* may be as large as f(n,M,W*) where n is the number of vertices and M is the maximum edge-weight. The function f is determined for the several variations of the Travelling Salesman's Problem and the bound is shown to be best possible in each case.

22 citations


Journal ArticleDOI
TL;DR: In this article, a heuristic formula for the asymptotic density of positive integers containing no arithmetic progression of k terms, generated by the greedy algorithm, was derived for the case where k is composite, and it was shown that for all e > 0, the number of elements of Sk which are less than n is greater than (1 − e)V2n for sufficiently large n.
Abstract: Let Sk be the set of positive integers containing no arithmetic progression of k terms, generated by the greedy algorithm. A heuristic formula, supported by compu- tational evidence, is derived for the asymptotic density of iS^ in the case where k is composite. This formula, with a couple of additional assumptions, is shown to imply that the greedy algorithm would not maximize S^p 1/n over all S with no arithmetic progression of k terms. Finally it is proved, without relying on any conjecture, that for all e > 0, the number of elements of Sk which are less than n is greater than (1 — e)V2n for sufficiently large n.

21 citations


Proceedings Article
01 Jan 1979
TL;DR: The paper addresses the problem of how to find the Greedy Triangulation efficiently in the average case and shows how in the worst case, the GT may be obtained in time O(n to the 3) and space O( n).
Abstract: The paper addresses the problem of how to find the Greedy Triangulation (GT) efficiently in the average case. It is noted that the problem is open whether there exists an efficient approximation algorithm to the Optimum Triangulation. It is first shown how in the worst case, the GT may be obtained in time O(n to the 3) and space O(n). Attention is then given to how the algorithm may be slightly modified to produce a time O(n to the 2), space O(n) solution in the average case. Finally, it is mentioned that Gilbert has found a worst case solution using totally different techniques that require space O(n to the 2) and time O(n to the 2 log n).

3 citations



Book ChapterDOI
01 Jan 1979
TL;DR: This paper deals with polynomial relations between different kinds of oracles for optimization problems over independence systems and establishes certain symmetry among problems and algorithms by dualization of independence systems.
Abstract: This paper deals with polynomial relations between different kinds of oracles for optimization problems over independence systems. Six different greedy algorithms as special oracle algorithms are also considered. A certain symmetry among problems and algorithms is established by dualization of independence systems.

3 citations


01 Jan 1979
TL;DR: The goal coordination technique of optimization theory for large-scale systems is used to develop a decentralized algorithm for optimal routing in datacomunication networks that solves the optimal flow assignment problem and provides the corresponding optimal routing.
Abstract: The goal coordination technique of optimization theory for large-scale systems is used to develop a decentralized algorithm for optimal routing in datacomunication networks. The algorithm is in two parts of which the first solves the optimal flow assignment problem and the second provides the corresponding optimal routing. All calculations are distributed among the nodes and require information only from adjacent nodes. The results are illustrated via an example and problems for future research are indicated.