Domination and total domination in complementary prisms

Let G be a graph and be the complement of G. The complementary prism of G is the graph formed from the disjoint union of G and by adding the edges of a perfect matching between the corresponding vertices of G and . For example, if G is a 5-cycle, then is the Petersen graph. In this paper we consider domination and total domination numbers of complementary prisms. For any graph G, and , where γ(G) and γ _t (G) denote the domination and total domination numbers of G, respectively. Among other results, we characterize the graphs G attaining these lower bounds. Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.     

A note on domination and total domination in prisms

Recently, Azarija et al. (Electron J Combin:1.19, 2017) considered the prism \(G \mathop {\square }K_2\) of a graph G and showed that \(\gamma _t(G \mathop {\square }K_2) = 2\gamma (G)\) if G is bipartite, where \(\gamma _t(G)\) and \(\gamma (G)\) are the total domination number and the domination number of G. In this note, we give a simple proof and observe that there are similar results for other pairs of parameters. We also answer a question from that paper and show that for all graphs \(\gamma _t(G \mathop {\square }K_2) \ge \frac{4}{3}\gamma (G)\), and this bound is tight.     

Complexity and Competition

Extensive‐form market games typically have a large number of noncompetitive equilibria. In this paper, we argue that the complexity of noncompetitive behavior provides a justification for competitive equilibrium in the sense that if rational agents have an aversion to complexity (at the margin), then maximizing behavior will result in simple behavioral rules and hence in a competitive outcome. For this purpose, we use a class of extensive‐form dynamic matching and bargaining games with a finite number of agents. In particular, we consider markets with heterogeneous buyers and sellers and deterministic, exogenous, sequential matching rules, although the results can be extended to other matching processes. If the complexity costs of implementing strategies enter players’ preferences lexicographically with the standard payoff, then every equilibrium strategy profile induces a competitive outcome.     

The Complexity of Forecast Testing

Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear‐time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature.     

企业合作复杂性与企业合作生态系统研究

简要回顾了组织生态的研究进展,认为不对称、自适应和管理困境这3个因素是引起企业合作复杂性的主要来源,并论述了制度生态因子、文化生态因子与技术生态因子对企业合作的影响,最后界定了企业合作生态系统的概念,并探讨了在企业合作生态系统中企业应该如何处理与其他个体的合作关系。     

Complexity,simplicity, simplexity

“In the midst of order, there is chaos; but in the midst of chaos, there is order”, John Gribbin wrote in his book Deep Simplicity (p. 76). In this dialectical spirit, we discuss the generative tension between complexity and simplicity in the theory and practice of management and organization. Complexity theory suggests that the relationship between complex environments and complex organizations advanced by the well-known Ashby’s law, may be reconsidered: only simple organization provides enough space for individual agency to match environmental turbulence in the form of complex organizational responses. We suggest that complex organizing may be paradoxically facilitated by a simple infrastructure, and that the theory of organizations may be viewed as resulting from the dialectical interplay between simplicity and complexity.     

Complexity theories and organizational change

Complexity theory or, more appropriately, theories, serves as an umbrella term for a number of theories, ideas and research programmes that are derived from scientific disciplines such as meteorology, biology, physics, chemistry and mathematics. Complexity theories are increasingly being seen by academics and practitioners as a way of understanding and changing organizations. The aim of this paper is to review the nature of complexity theories and their importance and implications for organizations and organizational change. It begins by showing how perspectives on organizational change have altered over the last 20 years. This is followed by an examination of complexity theories and their implications for organizational change. The paper concludes by arguing that, even in the natural sciences, the complexity approach is not fully developed or unchallenged, and that, as yet, organization theorists do not appear to have moved beyond the stage of using it as metaphor rather than as a mathematical way of analysing and managing organizations.     

More Large Accidents Through Complexity

Many would tend to characterize modern society as steeped in complexity. This complexity is seen by a number of professional people to imply risk-taking--or risk-making--on a high level. "A single mistake may give consequences of quite different proportions from earlier times," as one critic puts it. This hypothesis of increasing risks on a high level--of worst things getting worse--has been tested on fires in Sweden. Fire has always been a powerfully upsetting agent to the social fabric. Today industrial fires dominate the picture economically. The cost of industrial fires is about three times the cost of residential fires in Sweden. It is of interest to note that the damage cost of the worst fires (as measured in insurance payments) does not form an increasing part of overall fire damage costs, as one would expect from the above hypothesis. Whether the hypothesis holds with regard to indirect costs due to production stand-still is more uncertain. We can conclude that the potential of complexity to create large abnormal occurrences may have been somewhat prematurely announced--at least with regard to fires in Sweden.     

Multiperson Bargaining and Strategic Complexity

We investigate the effect of introducing costs of complexity in the n‐person unanimity bargaining game. As is well‐known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n & 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does limit the amount of delay that can occur in any agreement. In particular, we show that in any n‐player game, for any allocation z, an agreement on z at any period t can be sustained as a Nash equilibrium of the game with complexity costs if and only if t≤n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that ‘noisy Nash equilibrium’ with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.     

On pricing and protection of complementary products

The business literature advises firms producing complementary products to sell the core product at a low price, but to price the complementary product at a higher premium. This strategy, however, is problematic if firms face competitors in the market for complementary products as well, as observed in recent years for instance in the market for printers/ink cartridges. Motivated by several measures the firms have taken in this market, the current paper analyzes whether firms are interested in protecting their complementary product from outside competition. We find that firms protect their products only if consumers underestimate the demand for the complementary product when deciding which core product to buy. Moreover, we investigate how the decision to protect the complementary product interacts with a firm’s pricing decision. We show that the price policy proposed in the business literature should only be applied, if consumers sufficiently underestimate their demand for the complementary product so that firms strongly protect these products from outside competition.     

On the Complexity of Constructing Evolutionary Trees

In this paper we study a few important tree optimization problems with applications to computational biology. These problems ask for trees that are consistent with an as large part of the given data as possible. We show that the maximum homeomorphic agreement subtree problem cannot be approximated within a factor of , where N is the input size, for any 0 in polynomial time unless P = NP, even if all the given trees are of height 2. On the other hand, we present an O(N log N)-time heuristic for the restriction of this problem to instances with O(1) trees of height O(1) yielding solutions within a constant factor of the optimum. We prove that the maximum inferred consensus tree problem is NP-complete, and provide a simple, fast heuristic for it yielding solutions within one third of the optimum. We also present a more specialized polynomial-time heuristic for the maximum inferred local consensus tree problem.     

On the Complexity of the Steiner Problem

Recently Rubinstein et al. gave a new proof of the NP-completeness of the discretized Steiner problem, that is, the problem of finding a shortest network connecting a given set of points in the plane where all vertices are integer points and a discretized metric is used. Their approach was to consider the complexity of the PALIMEST problem, the Steiner problem for sets of points lying on two parallel lines. In this paper, we give a new proof of this theorem, using simpler, more constructive arguments. We then extend the result to a more general class of networks known as APE-Steiner trees in which certain angles between edges or slopes of edges are specified beforehand.     

Container Scheduling: Complexity and Algorithms

We consider the transport of containers through a fleet of ships. Each ship has a capacity constraint limiting the total number of containers it can carry and each ship visits a given set of ports following a predetermined route. Each container has a release date at its origination port, and a due date at its destination port. A container has a size 1 or size 2; size 1 represents a 1 TEU (20‐foot equivalent unit) and size 2 represents 2 TEUs. The delivery time of a container is defined as the time when the ship that carries the container arrives at its destination port. We consider the problem of minimizing the maximum tardiness over all containers. We consider three scenarios with regard to the routes of the ships, namely, the ships having (i) identical, (ii) nested, and (iii) arbitrary routes. For each scenario, we consider different settings for origination ports, release dates, sizes of containers, and number of ports; we determine the computational complexity of various cases. We also provide a simple heuristic for some cases, with its worst case analysis. Finally, we discuss the relationship of our problems with other scheduling problems that are known to be open.     

基于复杂性机理的移动商务系统思考

结合系统演化、技术创新理论,提出"主体-创新规律-组织方式"的移动商务复杂性思考框架.从移动信息在时间、空间方面的价值表现出发,围绕需求是技术创新的动力和约束规律,分析移动商务的必要参与主体和有效组织方式,从产业层面探讨移动商务复杂性机理.同时,应用本框架分析了移动商务产生及初期发展的现状,对中国目前移动商务存在的问题从产业链整体性、需求全面性和规制完善方面提出了解决途径.     

知识社会的企业生态系统复杂性

提出了企业生态系统生态学的研究框架,从复杂性科学的角度探讨了企业生态系统及其复杂性问题,并对知识社会企业生态系统复杂性以及知识社会复杂企业生态环境中的企业管理进行了分析.     

双寡头动态R&D竞争的复杂性研究

利用非线性动力系统的分支理论研究了有限理性双寡头动态R&D竞争模型,讨论了该模型Nash均衡点的存在性与稳定性,并对该模型进行了数值仿真.仿真结果表明,过大的R&D投入调整速度将导致系统出现倍岔、混沌等复杂的动力学现象;系统所处状态不同,则双寡头的R&D平均投入、平均利润的变化趋势也不一样;同时,R&D投入的调整速度对双寡头的前期利润以及R&D竞争到达均衡的时间均有显著影响.最后,应用延迟反馈控制法实现了对系统混沌态的控制.     

网络组织的复杂适应性研究

网络组织是企业组织发展的新趋势,它呈现出复杂适应系统的特征.本文在介绍复杂适应系统特征的基础上,研究了网络组织的复杂适应性,提出用基于Agent的建模仿真方法研究网络组织的思路,并构造了基于客户Agent与供应商Agent的简单仿真模型,希望探索一种新的研究思路,以丰富和深化网络组织的研究.     

基于TO视角的项目复杂性测度研究

在分析传统项目复杂性影响要素的基础上,从客观性任务和主观性组织的角度探讨了项目复杂性微观影响因子的TO概念模型;并基于ProjectSim建立了以隐性工作量表示的项目复杂性测度方法;然后以世博AB片区项目构建模型,对TO测度方法的假设进行验证,证实基于隐性工作量的项目复杂性测度方法正确有效。本研究丰富和发展了复杂项目管理理论,对大型复杂项目管理具有重要的理论指导意义。     

复杂科学与质量管理研究

系统科学对质量管理的重大贡献就是促成了全面质量管理的诞生与发展,而复杂科学是系统科学发展的新阶段,它主要是研究复杂性与复杂系统的科学。复杂科学必然对质量管理的发展起着十分重大的影响,本文就此进行一些初步的探讨。