We show that the convex hull of the set of feasible solutions of single-item capacitated lot-sizing problem (CLSP) is a base polyhedron of a polymatroid. We present a greedy algorithm to solve CLSP with linear objecti...
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We show that the convex hull of the set of feasible solutions of single-item capacitated lot-sizing problem (CLSP) is a base polyhedron of a polymatroid. We present a greedy algorithm to solve CLSP with linear objective function. The proposed algorithm is an effective implementation of the classical Edmonds' algorithm for maximizing linear function over a polymatroid. We consider some special cases of CLSP with nonlinear objective function that can be solved by the proposed greedy algorithm in O(n) time.
A two-step algorithm to solve the broadcast scheduling problem is presented. The first step employs finding a solution that has a transmission time slot for each station, while the second step attempts to maximise the...
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A two-step algorithm to solve the broadcast scheduling problem is presented. The first step employs finding a solution that has a transmission time slot for each station, while the second step attempts to maximise the throughput. Numerical examples that demonstrate the algorithm outperforms existing ones in terms of channel utilisation and packet delay are presented.
In the present paper we identify those filtered probability spaces (Omega, F, (F-n), P) that determine already the martingale type of a Banach space X. We isolate intrinsic conditions on the filtration (F-n) of purely...
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In the present paper we identify those filtered probability spaces (Omega, F, (F-n), P) that determine already the martingale type of a Banach space X. We isolate intrinsic conditions on the filtration (F-n) of purely atomic sigma-algebras which determine that the upper l(p) estimates parallel to f parallel to(p)(Lp(Omega, X)) <= C-p (parallel to E(f vertical bar F-0)parallel to(p)(Lp(Omega, X)) + Sigma(infinity)(n=1) parallel to E(f vertical bar F-n)- E(f vertical bar Fn-1)parallel to(p)(Lp(Omega,X))), f is an element of L-p(Omega, X) imply that the Banach space X is of martingale type p. Our paper complements G. Pisier's investigation [12] and continues the work by S. Geiss and second named author in [3]. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with It's stochastic delayed equations as the forward equations and anticipated backward stochastic differential ...
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The authors discuss one type of general forward-backward stochastic differential equations (FBSDEs) with It's stochastic delayed equations as the forward equations and anticipated backward stochastic differential equations as the backward equations. The existence and uniqueness results of the general FBSDEs are obtained. In the framework of the general FBSDEs in this paper, the explicit form of the optimal control for linearquadratic stochastic optimal control problem with delay and the Nash equilibrium point for nonzero sum differential games problem with delay are obtained.
This paper is concerned with the problem of finding optimal sub-routes from a set of predefined candidate transit routes with the objectives of maximizing transit ridership as well as minimizing operational costs. The...
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This paper is concerned with the problem of finding optimal sub-routes from a set of predefined candidate transit routes with the objectives of maximizing transit ridership as well as minimizing operational costs. The main contributions of this paper are: (1) considering transit ridership maximization in a multi-objective bi-level optimization framework;(2) proposing a greedy algorithm for the multi-objective design problem;(3) applying an efficient path-based algorithm to solve the lower level multi-modal traffic assignment problem. Numerical experiments indicate that the proposed algorithm is not only able to approximate the Pareto-optimal solutions with satisfactory accuracy, but also achieves a fast performance even for problems of real-world scale.
The total completion time of a task is also the major bottleneck in the big data processing applications based on parallel computation, since the computation and data are distributed on more and more nodes. Therefore,...
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The total completion time of a task is also the major bottleneck in the big data processing applications based on parallel computation, since the computation and data are distributed on more and more nodes. Therefore, the total completion time of task is an important index to evaluate the cloud performance. The access latency between the nodes is one of the key factors affecting task completion time for cloud applications. Additionally, minimising total access time can reduce the overall bandwidth cost of running the job. This paper proposes an optimisation model focused on optimising VMs placement so as to minimise the total data access latency where the datasets have been located. According to the proposed model, our optimising VMs problem is linear programming. Therefore, we obtain the optimum solution of our model by the branch-and-bound algorithm with time complexity O(2(N) (M)). Simultaneously, we also present a greedy algorithm, which has O(NM) of time complexity, to solve our model. Finally, the simulation results show that all of the solutions of our model are superior to existing models and close to the optimal value.
Morton et al. [1] describe a greedy algorithm for solving a class of cont ex programming problems. The algorithm is validated by the use of polymatroid theory. In the present paper we establish the validity of the alg...
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Morton et al. [1] describe a greedy algorithm for solving a class of cont ex programming problems. The algorithm is validated by the use of polymatroid theory. In the present paper we establish the validity of the algorithm by a more elementary argument using the well known Karush-Kuhn-Tucker optimality conditions. In [1] it is shown that a variant of the above mentioned greedy algorithm solves a related quadratic programming problem. Here we show that the variant in fact solves a slightly more general problem.
The paper investigates the uniform and almost everywhere convergence of the greedy algorithm by the Haar system. Necessary and sufficient conditions for norming the functions of Haar system are obtained, which guarant...
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The paper investigates the uniform and almost everywhere convergence of the greedy algorithm by the Haar system. Necessary and sufficient conditions for norming the functions of Haar system are obtained, which guarantee the uniform convergence for functions from C[0, 1] and almost everywhere convergence for functions from L(1)[0, 1].
An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in R-n. This model unifies various generalizations of combinatorial mo...
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An algebraic model generalizing submodular polytopes is presented, where modular functions on partially ordered sets take over the role of vectors in R-n. This model unifies various generalizations of combinatorial models in which the greedy algorithm and the Monge algorithm are successful and generalizations of the notions of core and Weber set in cooperative game theory. As a further application, we show that an earlier model of ours as well as the algorithmic model of Queyranne, Spieksma and Tardella for the Monge algorithm can be treated within the framework of usual matroid theory (on unordered ground-sets), which permits also the efficient algorithmic solution of the intersection problem within this model.
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