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Published in S. Sitharama Iyengar, Richard R. Brooks, Distributed Sensor Networks, 2016
Rajgopal Kannan, Costas Busch, Shuangqing Wei
In our previous work [8], we studied atomic bottleneck games. We proved that the PoS is 1. We showed that the PoA is bounded by O(L + log n), where L is the maximum allowed path length in 𝒫, and n is the number of nodes in the network. We also prove that κ ≤ PoA ≤ c(κ2 + log2n), where κ is the size of the largest edge-simple cycle in the graph and c is a constant. Some of the techniques that we propose (e.g., expansion) were used in an initial form in [8]. In an extension of this work, we consider in [6] wireless networks with routing classes Q1, …, Qψ, where each class j has a service cost Sj. Each path belongs to exactly one routing class. The player i cost function is Ci + Si, where Si is the cost of the service class of the path of i, and Ci is the congestion experienced by player i by considering only the paths in the same service class. The social cost function is the maximum player cost. We showed in [6] that such games stabilize with best response dynamics and the PoS is 1. The PoA is bounded by O(min(C*, S*) · ψ log n), where C* + S* is the optimal social cost. Such games can be used to provide approximations to the social cost function C + D, where D is the maximum path length in the routing. An improved version of this work is [7].
The method of routes and kinetic models
Published in Yu. G. Medvedevskikh, A.R. Kytsya, L.I. Bazylyak, A.A. Turovsky, G.E. Zaikov, Stationary and Non-Stationary Kinetics of the Photoinitiated Polymerization, 2004
Yu. G. Medvedevskikh, A.R. Kytsya, L.I. Bazylyak, A.A. Turovsky, G.E. Zaikov
Let us reiterate that among all possible cycles of a graph G={X,S} we investigate only the simple ones, since they do not contain other cycles, but realize the final chemical transformations in which the stoichiometric coefficients of the intermediate substances are equal to zero. A simple cycle is a closed route which does not contain the repeating ribs and a top. It follows from this, that the stoichiometric number of an elementary reaction in the simple cycle is equal only to 0,-1 or +1, depending on if the presented elementary reaction is included in a simple cycle and, if so, in which direction? Thus, the term “route” will be used for a simple cycle, that is a closed route which does not contain repeating ribs and a top of a graph G={X,S} representing the topology of a kinetic scheme.
Introduction
Published in Joseph Y.-T. Leung, Handbook of SCHEDULING, 2004
Notice that each nonzero entry A(i,j) has at most two links incident on itself, one horizontal and the other vertical. The number of possible types of isolated graph components consisting of such entries is three: isolated node, linear sequence, and simple cycle. Furthermore, the cycle always has an even number of vertices, since the odd cycle implies that some vertex must have two identical type of links, e.g., two horizontal (vertical) links, that do not exist in G. It is easy to observe that all the above types of graphs can be arranged as bipartite graphs.
Robust global distributed attitude control for multiple rigid bodies using a hybrid controller
Published in International Journal of Systems Science, 2020
Paulo P. M. Magro, Hugo Tadashi M. Kussaba, João Yoshiyuki Ishihara
Two simulations are considered: the first simulation illustrates some of the problems that may arise when the control strategy uses a continuous state feedback torque to stabilise disconnected reference points , and the second simulation exemplifies a scenario where the problems faced by the continuous controller in the previous scenario is not present to highlight the other advantages of the hybrid controller. The topology of communication in both simulations is shown in Figure 2.It is a simple cycle graph with nodes labelled from 1 to 6 referring to the six agents. The corresponding adjacency matrix of this graph is The inertia matrices considered in both simulations are the same and are shown in Table 1. In all simulations the control parameters were , , and , . The other parameters of the hybrid controller were chosen as and . The desired fixed reference was with .
Modeling and thermodynamic analysis of gas-supercritical carbon dioxide combined cycle system
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Jiayin Zhou, Diangui Huang, Yinke Qi
Figure 5 is a graph of top cycle efficiency and exhaust temperature as a function of pressure ratio, in which the black curve represents the simple cycle, and the colored curve represents the air preheating cycle with different regenerative degree (is regenerative degree, whose size is consistent with the energy efficiency of the top cycle regenerator). It can be seen from Figure 5 that the air preheating cycle within 0 to 40 pressure ratio with high thermal efficiency, when the pressure ratio is larger than 40, air preheating cycle compressor outlet temperature exceeds the turbine exhaust temperature, regenerator can no longer be in the turbine exhaust heat recovery for the air compressor export, so after the pressure ratio reaches back to the regeneration limit pressure ratio than, the air preheating cycle is not suitable. It can also be seen from the figure that as the air preheating cycle regenerative degree decreases, the change curve of its efficiency with the pressure ratio gradually moves closer to the simple cycle, and the optimal pressure ratio of the air preheating cycle efficiency gradually shifts to the right. When the regenerative degree decreases from 0.9 to 0.6, the optimum pressure ratio of efficiency increases from 20 to 35. Figure 5 shows the change curve of the exhaust temperature of the top cycle with the pressure ratio. It can be seen that when the regenerative degree is greater than 0.8, the exhaust temperature of the air preheating cycle increases continuously with the increase of the pressure ratio until it reaches the limit pressure ratio of the recuperation, then intersect with simple cycle. When it decreases from 0.8 to 0.6, the air preheating cycle curve gradually moves closer to the simple cycle, and the relationship between the exhaust temperature and the pressure ratio also transitions from increasing gradually to decreasing first and then increasing.
Off-line exploration of rectangular cellular environments with a rectangular obstacle
Published in Optimization Methods and Software, 2022
In this paper, the explored environment is assumed to be a rectangular polygon with a rectangular obstacle. We give a linear-time algorithm for exploring this environment that finds the tour of the optimal length. Our idea is, first, to find the longest simple cycle in the grid graph, then extending it to a tour that visits all the vertices of the graph. So we first explain how we compute the longest simple cycles.