scholarly journals Competitive Analysis for Two Variants of Online Metric Matching Problem

Author(s):  
Toshiya Itoh ◽  
Shuichi Miyazaki ◽  
Makoto Satake
Author(s):  
Toshiya Itoh ◽  
Shuichi Miyazaki ◽  
Makoto Satake

In the online metric matching problem, there are servers on a given metric space and requests are given one-by-one. The task of an online algorithm is to match each request immediately and irrevocably with one of the unused servers. In this paper, we pursue competitive analysis for two variants of the online metric matching problem. The first variant is a restriction where each server is placed at one of two positions, which is denoted by OMM([Formula: see text]). We show that a simple greedy algorithm achieves the competitive ratio of 3 for OMM([Formula: see text]). We also show that this greedy algorithm is optimal by showing that the competitive ratio of any deterministic online algorithm for OMM([Formula: see text]) is at least 3. The second variant is the online facility assignment problem on a line. In this problem, the metric space is a line, the servers have capacities, and the distances between any two consecutive servers are the same. We denote this problem by OFAL([Formula: see text]), where [Formula: see text] is the number of servers. We first observe that the upper and lower bounds for OMM([Formula: see text]) also hold for OFAL([Formula: see text]), so the competitive ratio for OFAL([Formula: see text]) is exactly 3. We then show lower bounds on the competitive ratio [Formula: see text] [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] for OFAL([Formula: see text]), OFAL([Formula: see text]) and OFAL([Formula: see text]), respectively.


2009 ◽  
Vol 35 (2) ◽  
pp. 186-192 ◽  
Author(s):  
Zhi-Bo TIAN ◽  
Li-Xin TANG ◽  
Yi-Ming REN ◽  
Yong-Ming ZHAO ◽  
Cheng-Xin WU
Keyword(s):  

2018 ◽  
pp. 48-52
Author(s):  
S. V. Popov ◽  
G. N. Devyatkov

When designing radioelectronic devices, that are included in the composition of various systems, it is important to solve broadband matching problem and filtering problem. However, usually these problems are separated and not considered together. Moreover, the synthesis of filters does not take into account the behavior of impedances of the generator and the load in the stopbands. The solution of the complex problem is actual, since it allows expanding the functionality of the device, which can greatly simplify the construction of the radio engineering product. It should be noted that in the known literature solution of this problem in such a formulation is not considered. The aim of the work is to develop a synthesis method and algorithm of broadband devices that connect arbitrary immitances of the generator and the load, and these devices should perform simultaneously functions of both matching and filtering in reactive lumped electric element base and in distributed electric element base, limited only by transmission lines with T-waves. In this paper, a two-stage automated method of synthesis presented here stage allows at the first to adequately find a good initial solution to the posed problem (determining structure and parameters of the broadband matching and filtering quadrupole), in the second stage this approach allows to find the optimal solution to the complex problem, taking into account the constraints on physical and circuit realizability. In this work, the synthesis of broadband matching and filtering devices in lumped and distributed electrical element basis is carried out, and these devices connect complex impedances of the source and the load. The characteristics of the devices obtained after the synthesis show that the solution of the complex problem of matching and filtering gives a significant improvement in filtering properties with small losses in the level of transmitted power.


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