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Constrained Sequential Resource Allocation and Guessing Games

IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第11期54卷 4946-4965页

作者： Chang, Nicholas B. Liu, Mingyan Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

In this paper, we consider a constrained sequential resource allocation problem where an individual needs to accomplish a task by repeatedly guessing/investing a sufficient level of effort/input. If the investment falls short of a minimum required level that is unknown to the individual, she fails;with each unsuccessful attempt, the individual then increases the input and tries again until she succeeds. The objective is to complete the task with as little resources/cost as possible subject to a delay constraint. The optimal strategy lies in the proper balance between 1) selecting a level (far) below the minimum required and therefore having to try again, thus wasting resources, and 2) selecting a level (far) above the minimum required, and therefore, overshooting and wasting resources. A number of motivating applications arising from communication networks are provided. Assuming that the individual has no knowledge on the distribution of the minimum effort required to complete the task, we adopt a worst-case cost measure and a worst-case delay measure to formulate the above constrained optimization problem. We derive a class of optimal strategies, shown to be randomized, and obtain their performance as a function of the constraint.

关键词： Competitive analysis constrained optimization data query and search exponential functions minimax problems online algorithms randomized algorithms stochastic analysis

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Controlled flooding search with delay constraints

Controlled flooding search with delay constraints

引用

IEEE INFOCOM 2006 Conference/25th IEEE International Conference on Computer Communications

作者： Chang, Nicholas B. Liu, Mingyan Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

ISBN: (纸本)9781424402212

In this paper we consider the problem of query and search in a network, e.g., searching for a specific node or a piece of data. We limit our attention to the class of TTL (time-to-live) based controlled flooding search strategies where query/search packets are broadcast and relayed in the network until a preset TTL value carried in the packet expires. Every unsuccessful search attempt results in an increased TTL value (i.e., larger search area) and the same process is repeated. Every search attempt also incurs a cost (in terms of packet transmissions and receptions) and a delay (time till timeout or till the target is found). The primary goal is to derive search strategies (i.e., sequences of TTL values) that minimize a worst-case cost measure subject to a worst-case delay constraint. We present a constrained optimization framework and derive a class of optimal strategies, shown to be randomized strategies, and obtain their performance as a function of the delay constraint. We also use these results to discuss the trade-off between search cost and delay within the context of flooding search.

关键词： data query and search TTL controlled flooding search wireless sensor and ad hoc networks constrained optimization randomized strategy competitive analysis

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