This paper proposes a polynomial -timealgorithm for a server allocation problem in delay -sensitive Internet -ofThings (IoT) monitoring services. The server allocation problem determines the appropriate servers to wh...
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This paper proposes a polynomial -timealgorithm for a server allocation problem in delay -sensitive Internet -ofThings (IoT) monitoring services. The server allocation problem determines the appropriate servers to which the database and application are allocated to minimize the maximum delay between the latest update of reference data and the start of application processing for monitoring data. The server allocation problem was previously handled by expressing it as an integer linear programming (ILP) problem. Nevertheless, it fails to meet the computational time complexity needed to solve the problem, and it does not offer a more efficient technique than the ILP approach. The proposed algorithm consists of two components. The first step entails choosing utilization servers for both the database and the application. Next, the second phase entails matching each usage server and its corresponding IoT device. We prove that the proposed algorithm obtains an optimal solution in polynomialtime. We compare computation times between the ILP approach and the proposed algorithm. Numerical results show that the proposed algorithm obtains the optimal solution faster than the ILP approach.
We consider an optimization problem arising when a set of items must be selected and picked up from given locations in an automated storage and retrieval system by a crane of given capacity, minimizing the overall dis...
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We consider an optimization problem arising when a set of items must be selected and picked up from given locations in an automated storage and retrieval system by a crane of given capacity, minimizing the overall distance traveled. The problem has been classified as open in a recent taxonomy of optimal picking problems in automated warehouses. In this paper, we analyze some non-trivial properties of the problem and we describe a polynomial-time dynamic programming algorithm to solve it to proven optimality.
We consider the problem to schedule n coupled-tasks in presence of treatment tasks. This work is motivated by the problem of data acquisition for a torpedo. In such context, we developp a O(nlog(n)) polynomial-time al...
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A polynomial-time algorithm for a class of linear complementarity problems with positive semidefinite matrices is presented. The method is based on a one-step Euler's prediction and one-step Newton's correctio...
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A polynomial-time algorithm for a class of linear complementarity problems with positive semidefinite matrices is presented. The method is based on a one-step Euler's prediction and one-step Newton's correction procedure to follow the homotopy path defined as the set {(x, y) epsilon R-+(n): x(i)Y(i)=mu, i = 1,.., n, mu > 0, y = Mx + q}, and solves the problem in O(n(3.5)L) arithmetic operations. Moreover, after one iteration the value x(T)y decreases with the ratio at least (1-(2/5 root n)).
We consider m identical machines scheduling problems with fully parallel jobs. Each job Jj requires processing time pj and can be executed on any machine at any time unit. In this paper, four scheduling problems are c...
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Given two graphs, Subgraph Isomorphism is the problem of deciding whether the first graph (the base graph) contains a subgraph isomorphic to the second graph (the pattern graph). This problem is NP-complete for very r...
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ISBN:
(纸本)9783319060897;9783319060880
Given two graphs, Subgraph Isomorphism is the problem of deciding whether the first graph (the base graph) contains a subgraph isomorphic to the second graph (the pattern graph). This problem is NP-complete for very restricted graph classes such as connected proper interval graphs. Only a few cases are known to be polynomial-time solvable even if we restrict the graphs to be perfect. For example, if both graphs are co-chain graphs, then the problem can be solved in linear time. In this paper, we present a polynomial-time algorithm for the case where the base graphs are chordal graphs and the pattern graphs are co-chain graphs. We also present a linear-timealgorithm for the case where the base graphs are trivially perfect graphs and the pattern graphs are threshold graphs. These results answer some of the open questions of Kijima et al. [Discrete Math. 312, pp. 3164-3173, 2012]. To present a complexity contrast, we then show that even if the base graphs are somewhat restricted perfect graphs, the problem of finding a pattern graph that is a chain graph, a co-chain graph, or a threshold graph is NP-complete.
Let G=(V,E) be a graph where V and E are the vertex and edge sets, respectively. For two disjoint subsets A and B of V, we say AdominatesB if every vertex of B is adjacent to at least one vertex of A in G. A vertex pa...
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Exponential runtimes of algorithms for values for games with transferable utility like the Shapley value are one of the biggest obstacles in the practical application of otherwise axiomatically convincing solution con...
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Exponential runtimes of algorithms for values for games with transferable utility like the Shapley value are one of the biggest obstacles in the practical application of otherwise axiomatically convincing solution concepts of cooperative game theory. We investigate to what extent the hierarchical structure of a level structure improves runtimes compared to an unstructured player set. Representatively, we examine the Shapley levels value, the nested Shapley levels value, and, as a new value for level structures, the nested Owen levels value. For these values, we provide polynomial-time algorithms (under normal conditions) which are exact and therefore not approximation algorithms. Moreover, we introduce relevant coalition functions where all coalitions that are not relevant for the payoff calculation have a Harsanyi dividend of zero. Our results shed new light on the computation of values of the Harsanyi set as the Shapley value and many values from extensions of this set. (C) 2021 Elsevier B.V. All rights reserved.
In the path movement problem, we are given an undirected graph G = (V, E), a source vertex s, a destination vertex t, and a set of movable objects, called pebbles, which are placed on a subset of the vertices of a gra...
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In the path movement problem, we are given an undirected graph G = (V, E), a source vertex s, a destination vertex t, and a set of movable objects, called pebbles, which are placed on a subset of the vertices of a graph. We want to move a subset of the pebbles along the edges to a subset of the vertices of the graph such that there exists a path from s to t in graph G in such a way that all the vertices in that path are occupied by at least one pebble. The PathMax and the PathSum problems are the path movement problems in which we want to minimize the maximum movements and the total movements made by the pebbles, respectively. In [7], the researchers proved that both the problems are NP-hard in general graphs. In this paper, the PathMax and the PathSum problems are considered on special classes of graph G, that is, G is a tree and a unicyclic graph. More precisely, this paper shows that PathMax and PathSum problems can be easily solved in polynomialtime when the input graph is a tree or a unicyclic graph.
The computational challenge offered by many traditional network flow models is modest, and large-scale instances can be solved fast. When the composition of the flow is part of the model, the required computation time...
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The computational challenge offered by many traditional network flow models is modest, and large-scale instances can be solved fast. When the composition of the flow is part of the model, the required computation time may increase substantially. This is in particular true for the pooling problem, where the relative content of certain flow components is restricted. Flow entering the network at the source nodes has a given composition, whereas the composition in other nodes is determined by the composition of entering flows. At the network terminals, the flow composition is subject to restrictions referred to as quality constraints. The pooling problem is known to be strongly NP-hard, even if the network has only one pool, but is solvable in polynomialtime if also the number of terminals or the number of quality parameters (flow components) is bounded. The problem is also NP-hard if there are only two sources and terminals and only one quality parameter. Two related questions have been left open in the literature so far. For the single-pool version, it has not been known whether the problem is solvable in polynomialtime if the number of sources is bounded. For the version with a single quality parameter and two sources and terminals, the question whether a pseudo-polynomialalgorithm exists has been open. This paper gives positive answers to both questions.
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