We propose a polynomial algorithm for linear feasibility problems. The algorithm represents a linear problem in the form of a system of linear equations and non-negativity constraints. Then it uses a procedure which e...
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We propose a polynomial algorithm for linear feasibility problems. The algorithm represents a linear problem in the form of a system of linear equations and non-negativity constraints. Then it uses a procedure which either finds a solution for the respective homogeneous system or provides the information based on which the algorithm rescales the homogeneous system so that its feasible solutions in the unit cube get closer to the vector of all ones. In a polynomial number of calls to the procedure the algorithm either proves that the original system is infeasible or finds a solution in the relative interior of the feasible set.
A polynomial time algorithm is presented for solving the following two-variable ineger programming problem maximize [formula-omitted] integers, where a,j, cj, and b, are assumed to be nonnegattve integers This generah...
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A polynomial filtering algorithm is proposed to solve a sea vehicle navigation problem using information on the range and radial velocity with respect to a fixed beacon, formulated in the context of the Bayesian appro...
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A polynomial filtering algorithm is proposed to solve a sea vehicle navigation problem using information on the range and radial velocity with respect to a fixed beacon, formulated in the context of the Bayesian approach An example of practical implementation of the designed algorithm is considered. It is shown that the accuracy of the polynomial algorithm is close to that calculated by method of statistical tests with the use of a particle filter;in comparison, the Extended Kalman filter (EKF) yields a worse result. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
In this paper, we develop two algorithms for finding a directed path of minimum rank-two monotonic cost between two specified nodes in a network with n nodes and m arcs. Under the condition that one of the vectors cha...
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In this paper, we develop two algorithms for finding a directed path of minimum rank-two monotonic cost between two specified nodes in a network with n nodes and m arcs. Under the condition that one of the vectors characterizing the cost function f is binary, one yields an optimal solution in O(n(3)) or O(nm log n) time if f is quasiconcave;the other solves any problem in O(nm + n(2) log n) time.
We highlight in this article the relevance of a decision problem in k-cyclic robotic scheduling: deciding whether a certain throughput is feasible or not. Research until now has been focused mainly on the optimization...
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We highlight in this article the relevance of a decision problem in k-cyclic robotic scheduling: deciding whether a certain throughput is feasible or not. Research until now has been focused mainly on the optimization problem (finding the maximum possible throughput). We provide an algorithm for this decision problem in 2-cyclic robotic scheduling that runs in O(n3) time, where n is the number of machines in the production line, and we outline possibilities for further work in this direction.
Clique partitioning in Euclidean space R-n consists in finding a partition of a given set of N points into M clusters in order to minimize the sum of within-cluster interpoint distances. For n = 1 clusters need not co...
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Clique partitioning in Euclidean space R-n consists in finding a partition of a given set of N points into M clusters in order to minimize the sum of within-cluster interpoint distances. For n = 1 clusters need not consist of consecutive points on a line but have a nestedness property. Exploiting this property, an O((NM2)-M-5) dynamic programming algorithm is proposed. A theta(N) algorithm is also given for the case M = 2. (C) 2002 Published by Elsevier Science B.V.
Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We sho...
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Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an O(n log n)-time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.
Recently, Frumkin [9] pointed out that none of the well-known algorithms that transform an integer matrix into Smith [16] or Hermite [12] normal form is known to be polynomially bounded in its running time. In fact, B...
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Recently, Frumkin [9] pointed out that none of the well-known algorithms that transform an integer matrix into Smith [16] or Hermite [12] normal form is known to be polynomially bounded in its running time. In fact, Blankinship [3] noticed—as an empirical fact—that intermediate numbers may become quite large during standard calculations of these canonical forms. Here we present new algorithms in which both the number of algebraic operations and the number of (binary) digits of all intermediate numbers are bounded by polynomials in the length of the input data (assumed to be encoded in binary). These algorithms also find the multiplier-matrices K, U
Smith normal form
Hermite normal form
polynomial algorithm
Greatest Common Divisor
matrix-triangulation
matrix diagonalization
integer matrices
computational complexity
A variation on the Edmonds-Karp scaling approach to the minimum cost network flow problem is examined. This algorithm, which scales costs rather than right-hand sides, also runs in polynomial time. Large-scale computa...
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A variation on the Edmonds-Karp scaling approach to the minimum cost network flow problem is examined. This algorithm, which scales costs rather than right-hand sides, also runs in polynomial time. Large-scale computational experiments indicate that the computational behavior of such scaling algorithms may be much better than had been presumed. Within several distributions of square, dense, capacitated transportation problems, a cost scaling code, SCALE, exhibits linear growth in average execution time with the number of edges, while two network simplex codes, RNET and GNET, exhibit greater than linear growth. Our experiments reveal that median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated. Moreover, for fixed problem size, individual execution times appear to behave as through they are approximately lognormally distributed with constant variance. The experiments also reveal sensitivity of the parameters in the models, and in the models themselves, to variations in the distribution of problems. This argues for caution in the interpretation of such computational studies beyond the realm in which the computations were performed.
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