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781.
The global factory literature suggests that MNCs can take advantage of global operations by extensively offshoring and outsourcing activities. However, the added difficulty for the lead firm to coordinate the resulting complex structure is often underestimated. Evidence could be found in Boeing's 787 Dreamliner project, in which the external complexity disrupted MNC performance. Motivated by the gap between theory and practice, this study focuses on systems of MNCs connected with each other with supplier-client relationships and/or outsourcing. In particular it investigates the interplay of the internal and external complexity in such systems and how their balance affects the system performance. The study models the internal and external complexity by using the NKC-simulation methodology and adjusting it to the specific MNC context. The NKC methodology is widely used in organization theory to study complex systems. Simulations comparing the performance of MNCs that use outsourcing to different degrees indicate that a balanced level of internal and external complexity is beneficial in the context of global factory. 相似文献
782.
In the facility location game on a line, there are some agents who have fixed locations on the line where an obnoxious facility will be placed. The objective is to maximize the social welfare, e.g., the sum of distances from the facility to all agents. On collecting location information, agents may misreport the locations so as to stay far away from the obnoxious facility. In this paper, strategy-proof mechanisms are designed and the approximation ratio is used to measure the performances of the strategy-proof mechanisms. Two objective functions, maximizing the sum of squares of distances (maxSOS) and maximizing the sum of distances (maxSum), have been considered. For maxSOS, a randomized 5/3-approximated strategy-proof mechanism is proposed, and the lower bound of the approximation ratio is proved to be at least 1.042. For maxSum, the lower bound of the approximation ratio of the randomized strategy-proof mechanism is proved to be 1.077. Moreover, a general model is considered that each agent may have multiple locations on the line. For the objective functions maxSum and maxSOS, both deterministic and randomized strategy-proof mechanisms are investigated, and the deterministic mechanisms are shown to be best possible. 相似文献
783.
Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g. in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics define an edge-colored complete graph that allows to represent the topology of this graph as a vertex-colored tree. Here, we are interested in the structure and the complexity of certain combinatorial problems resulting from considerations based on symbolic ultrametrics, and on algorithms to solve them.This includes, the characterization of symbolic ultrametrics that additionally distinguishes between edges and non-edges of arbitrary edge-colored graphs G and thus, yielding a tree representation of G, by means of so-called cographs. Moreover, we address the problem of finding “closest” symbolic ultrametrics and show the NP-completeness of the three problems: symbolic ultrametric editing, completion and deletion. Finally, as not all graphs are cographs, and hence, do not have a tree representation, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of an arbitrary non-cograph G. This is equivalent to find an optimal cograph edge k-decomposition \(\{E_1,\dots ,E_k\}\) of E so that each subgraph \((V,E_i)\) of G is a cograph. We investigate this problem in full detail, resulting in several new open problems, and NP-hardness results.For all optimization problems proven to be NP-hard we will provide integer linear program formulations to solve them. 相似文献
784.
A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. The domination number of D, denoted by \(\gamma (D)\), is the minimum cardinality of a dominating set of D. The Slater number \(s\ell (D)\) is the smallest integer t such that t added to the sum of the first t terms of the non-increasing out-degree sequence of D is at least as large as the order of D. For any digraph D of order n with maximum out-degree \(\Delta ^+\), it is known that \(\gamma (D)\ge \lceil n/(\Delta ^++1)\rceil \). We show that \(\gamma (D)\ge s\ell (D)\ge \lceil n/(\Delta ^++1)\rceil \) and the difference between \(s\ell (D)\) and \(\lceil n/(\Delta ^++1)\rceil \) can be arbitrarily large. In particular, for an oriented tree T of order n with \(n_0\) vertices of out-degree 0, we show that \((n-n_0+1)/2\le s\ell (T)\le \gamma (T)\le 2s\ell (T)-1\) and moreover, each value between the lower bound \(s\ell (T)\) and the upper bound \(2s\ell (T)-1\) is attainable by \(\gamma (T)\) for some oriented trees. Further, we characterize the oriented trees T for which \(s\ell (T)=(n-n_0+1)/2\) hold and show that the difference between \(s\ell (T)\) and \((n-n_0+1)/2\) can be arbitrarily large. Some other elementary properties involving the Slater number are also presented. 相似文献
785.
Marin Bougeret Guillerme Duvillié Rodolphe Giroudeau 《Journal of Combinatorial Optimization》2018,36(3):1059-1073
In this paper we consider the multidimensional binary vector assignment problem. An input of this problem is defined by m disjoint multisets \(V^1, V^2, \ldots , V^m\), each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each multiset \(V^i\). To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. We denote this problem by Open image in new window , and the restriction of this problem where every vector has at most c zeros by Open image in new window . Open image in new window was only known to be Open image in new window -hard, even for Open image in new window . We show that, assuming the unique games conjecture, it is Open image in new window -hard to Open image in new window -approximate Open image in new window for any fixed Open image in new window and Open image in new window . This result is tight as any solution is a Open image in new window -approximation. We also prove without assuming UGC that Open image in new window is Open image in new window -hard even for Open image in new window . Finally, we show that Open image in new window is polynomial-time solvable for fixed Open image in new window (which cannot be extended to Open image in new window ). 相似文献
786.
An oriented graph \(G^\sigma \) is a digraph without loops or multiple arcs whose underlying graph is G. Let \(S\left( G^\sigma \right) \) be the skew-adjacency matrix of \(G^\sigma \) and \(\alpha (G)\) be the independence number of G. The rank of \(S(G^\sigma )\) is called the skew-rank of \(G^\sigma \), denoted by \(sr(G^\sigma )\). Wong et al. (Eur J Comb 54:76–86, 2016) studied the relationship between the skew-rank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skew-rank, the independence number, and some other parameters are considered. First we show that \(sr(G^\sigma )+2\alpha (G)\geqslant 2|V_G|-2d(G)\), where \(|V_G|\) is the order of G and d(G) is the dimension of cycle space of G. We also obtain sharp lower bounds for \(sr(G^\sigma )+\alpha (G),\, sr(G^\sigma )-\alpha (G)\), \(sr(G^\sigma )/\alpha (G)\) and characterize all corresponding extremal graphs. 相似文献
787.
Because of its application in the field of security in wireless sensor networks, k-path vertex cover (\(\hbox {VCP}_k\)) has received a lot of attention in recent years. Given a graph \(G=(V,E)\), a vertex set \(C\subseteq V\) is a k-path vertex cover (\(\hbox {VCP}_k\)) of G if every path on k vertices has at least one vertex in C, and C is a connected k-path vertex cover of G (\(\hbox {CVCP}_k\)) if furthermore the subgraph of G induced by C is connected. A homogeneous wireless sensor network can be modeled as a unit disk graph. This paper presents a new PTAS for \(\hbox {MinCVCP}_k\) on unit disk graphs. Compared with previous PTAS given by Liu et al., our method not only simplifies the algorithm and reduces the time-complexity, but also simplifies the analysis by a large amount. 相似文献
788.
A 2-distance k-coloring of a graph G is a proper k-coloring such that any two vertices at distance two get different colors. \(\chi _{2}(G)\)=min{k|G has a 2-distance k-coloring}. Wegner conjectured that for each planar graph G with maximum degree \(\Delta \), \(\chi _2(G) \le 7\) if \(\Delta \le 3\), \(\chi _2(G) \le \Delta +5\) if \(4\le \Delta \le 7\) and \(\chi _2(G) \le \lfloor \frac{3\Delta }{2}\rfloor +1\) if \(\Delta \ge 8\). In this paper, we prove that: (1) If G is a planar graph with maximum degree \(\Delta \le 5\), then \(\chi _{2}(G)\le 20\); (2) If G is a planar graph with maximum degree \(\Delta \ge 6\), then \(\chi _{2}(G)\le 5\Delta -7\). 相似文献
789.
Mohammed-Albarra Hassan Imed Kacem Sébastien Martin Izzeldin M. Osman 《Journal of Combinatorial Optimization》2018,36(3):1074-1101
In this paper we study the m-clique free interval subgraphs. We investigate the facial structure of the polytope defined as the convex hull of the incidence vectors associated with these subgraphs. We also present some facet-defining inequalities to strengthen the associated linear relaxation. As an application, the generalized open-shop problem with disjunctive constraints (GOSDC) is considered. Indeed, by a projection on a set of variables, the m-clique free interval subgraphs represent the solution of an integer linear program solving the GOSDC presented in this paper. Moreover, we propose exact and heuristic separation algorithms, which are exploited into a Branch-and-cut algorithm for solving the GOSDC. Finally, we present and discuss some computational results. 相似文献
790.
The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index \(M_2^{\alpha }\), and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randi?, the second Zagreb and the modified Zagreb indices. 相似文献