Based on the nearest-point projection of geometric convexity we give a general projection approach for solving the feasibility problem of linear programming. Application of Shor's method of space dilation gives ri...
详细信息
Based on the nearest-point projection of geometric convexity we give a general projection approach for solving the feasibility problem of linear programming. Application of Shor's method of space dilation gives rise to a family of polynomial-time ellipsoidal algorithms with improved termination criteria in case of infeasibility. Moreover, the approach renders possible application of various techniques from nonlinear programming. In particular, using a variable metric algorithm with exact line search we obtain a fast and practically well-behaving algorithm for linear programming.
The paper introduces the two-machine super-shop scheduling problem to minimize makespan. The well-known flow-shop, open-shop, job-shop and mixed-shop scheduling problems are special cases of our model. A polynomial-ti...
详细信息
The paper introduces the two-machine super-shop scheduling problem to minimize makespan. The well-known flow-shop, open-shop, job-shop and mixed-shop scheduling problems are special cases of our model. A polynomial-time algorithm to find both pre-emptive and non-pre-emptive optimal schedules is described.
An extension of the Economic Order Quantity (EOQ) model to multi-stage production-distribution systems and the isotonic regression problem are known to be equivalent and to be solvable in O(N4) time. The following spe...
详细信息
An extension of the Economic Order Quantity (EOQ) model to multi-stage production-distribution systems and the isotonic regression problem are known to be equivalent and to be solvable in O(N4) time. The following specializations of the model are solvable in O(N log N) time: joint replenishment systems, pure assembly systems, nested policies in pure distribution systems, nonnested policies in one-warehouse multi-retailer systems, nested policies in multi-item, one-warehouse, multi-retailer systems, and system in which the underlying network is a series-parallel digraph. We show here that a generalization of this problem is solvable in O(N log N) time whenever the undirected version of the underlying network is a tree. The algorithm we proposed is used as a subroutine in an algorithm solving the EOQ problem on general circuitless directed graphs, the subject of a companion paper.
Given 2 disjoint graphs and a vertex w in the first graph, the graph G obtained by first removing w from the first graph and then making every vertex in the 2nd graph adjacent to all the neighbors of w in the first gr...
详细信息
Given 2 disjoint graphs and a vertex w in the first graph, the graph G obtained by first removing w from the first graph and then making every vertex in the 2nd graph adjacent to all the neighbors of w in the first graph is said to arise by substitution from the first graph to the 2nd. The theoretical importance of substitution was highlighted by Lovasz (1972). His fundamental result asserting that a graph is perfect if and only if its complement is perfect relies on the fact that substitution preserves perfection. Moreover, detecting whether a graph G is substitution-composite can be done in polynomialtime. A characterization of forbidden configurations of the closure of triangle-free graphs (strictly containing the bipartite graphs) under substitution is presented.
Given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the t...
详细信息
Given a finite undirected graph with nonnegative edge capacities the minimum capacity cut problem consists of partitioning the graph into two nonempty sets such that the sum of the capacities of edges connecting the two parts is minimum among all possible partitionings. The standard algorithm to calculate a minimum capacity cut, due to Gomory and Hu (1961), runs in O(n 4) time and is difficult to implement. We present an alternative algorithm with the same worst-case bound which is easier to implement and which was found empirically to be far superior to the standard algorithm. We report computational results for graphs with up to 2000 nodes.
A new interior point method for the solution of the linear programming problem is presented. It is shown that the method admits a polynomialtime bound. The method is based on the use of the trajectory of the problem,...
详细信息
A new interior point method for the solution of the linear programming problem is presented. It is shown that the method admits a polynomialtime bound. The method is based on the use of the trajectory of the problem, which makes it conceptually very simple. It has the advantage above related methods that it requires no problem transformation (either affine or projective) and that the feasible region may be unbounded. More importantly, the method generates at each stage solutions of both the primal and the dual problem. This implies that, contrary to the simplex method, the quality of the present solution is known at each stage. The paper also contains a practical (i.e., deepstep) version of the algorithm.
We describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of \(O\left( {\sqrt n L} \right)\)number of iterations, whereL is the input size. Each iteration upd...
详细信息
We describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of \(O\left( {\sqrt n L} \right)\)number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea. The total number of arithmetic operations is shown to be of the order of O(n 3 L).
We describe a primal-dual interior point algorithm for linear programming problems which requires a total of \(O\left( {\sqrt n L} \right)\)number of iterations, whereL is the input size. Each iteration updates a pen...
详细信息
We describe a primal-dual interior point algorithm for linear programming problems which requires a total of \(O\left( {\sqrt n L} \right)\)number of iterations, whereL is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. The algorithm is based on the path following idea.
The main result of this paper is an 0([V] x [E]) time algorithm for deciding whether a given graph is a circle graph, that is, the intersection graph of a set of chords on a circle. The algorithm utilizes two new grap...
详细信息
The main result of this paper is an 0([V] x [E]) time algorithm for deciding whether a given graph is a circle graph, that is, the intersection graph of a set of chords on a circle. The algorithm utilizes two new graph-theoretic results, regarding necessary induced subgraphs of graphs having neither articulation points nor similar pairs of vertices. Furthermore, as a substep of the algorithm, it is shown how to find in 0([V] x [E]) time a decomposition of a graph into prime graphs, thereby improving on a result of Cunningham.
Papadimitriou and Steiglitz constructed ‘traps’ for the symmetric travelling salesman problem (TSP) with n = 8 k cities. The constructed problem instances have exponentially many suboptimal solutions with arbitraril...
详细信息
Papadimitriou and Steiglitz constructed ‘traps’ for the symmetric travelling salesman problem (TSP) with n = 8 k cities. The constructed problem instances have exponentially many suboptimal solutions with arbitrarily large weight, which differ from the unique optimal solution in exactly 3 k edges, and hence local search algorithms are ineffective to solve this problem. However, we show that this class of ‘catastrophic’ examples can be solved by linear programming relaxation appended with k subtour elimination constraints. It follows that this class of problem instances of TSP can be optimized in polynomialtime.
暂无评论