Online request server matching
نویسنده
چکیده
In this report we study a new variant of an online bipartite matching problem, which can be interpreted as a scheduling problem. Then, we have one resource, called server, which is available for one unit in every step of a discrete time model. At most one task with unit demand can occur per time step. It is called request, and speciies a set of time steps when the serving is accepted. These times must not be situated in the past and neither need to be consecutive nor include the time of the arrival of the request. After the arrival of a request in time step i, an online algorithm has to decide which request will be served in step i. This decision has to be made without knowledge of future requests. The objective is a maximization of the number of served requests. It is obvious, how to model this scheduling problem with a matching problem in a bipartite graph. However, this online bipartite matching problem diiers considerably from the model in KVV90]. So we call our model online request server matching (ORSM). Indeed, it is a special case of the roommates problem, that was introduced in BR93]. To investigate the ORSM problem, we use competitive analysis. A lower bound of the competitive ratio of 1.5 is shown, and an optimal 1.5-competitive online algorithm is presented. Additionally, a weighted variant of the ORSM problem (wORSM) is investigated. Here, every edge has a weight and the objective is the online construction of a matching with maximal overall weight. For the wORSM problem a general lower bound of 1.618 for the competitive ratio is shown. A presented online algorithm is proven to be 2-competitive. A few concluding remarks and a discussion of open problems complete this report.
منابع مشابه
A Robust and Optimal Online Algorithm for Minimum Metric Bipartite Matching
We study the Online Minimum Metric Bipartite Matching Problem. In this problem, we are given point sets S and R which correspond to the server and request locations; here |S| = |R| = n. All these locations are points from some metric space and the cost of matching a server to a request is given by the distance between their locations in this space. In this problem, the request points arrive one...
متن کاملOnline Bottleneck Matching
We consider the online bottleneck matching problem, where k serververtices lie in a metric space and k request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. The goal is to minimize the maximum distance between any request and its server. Because no algorithm can have a competitive ratio better thanO(k) for this problem, we use resource augmenta...
متن کاملThe Power of Rejection in Online Bottleneck Matching
We consider the online matching problem, where n server-vertices lie in a metric space and n request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. We focus on the egalitarian bottleneck objective, where the goal is to minimize the maximum distance between any request and its server. It has been demonstrated that while there are effective algori...
متن کاملServe or skip: the power of rejection in online bottleneck matching
We consider the online matching problem, where n server-vertices lie in a metric space and n request-vertices that arrive over time each must immediately be permanently assigned to a server-vertex. We focus on the egalitarian bottleneck objective, where the goal is to minimize the maximum distance between any request and its server. It has been demonstrated that while there are effective algori...
متن کاملOnline Matching for Scheduling Problems
In this work an alternative online variant of the matching problem in bipartite graphs is presented. It is motivated by a scheduling problem in an online environment. In such an environment, a task is unknown up to its disclosure. However, in that moment it is not necessary to take a decision on the service of that particular task. In reality, an online scheduler has to decide on how to use the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 268 شماره
صفحات -
تاریخ انتشار 2001