A PTAS for delay minimization in establishing wireless conference calls

Epstein, Leah; Levin, Asaf

doi:10.1016/j.disopt.2007.11.004

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…Recall that the number of combinations of general types and permutations is at most m!m ε 2m , thus the additive factor is at most m!m ε 2m (2m! + 1)ε 2m+5 ≤ ε 4 . Summarizing we get,…”

Section: Usersmentioning

confidence: 99%

“…Bar-Noy and Malewicz [2] suggested a simple algorithm which combines users and reduces to the algorithm for the case m = 1. This is a 4 3 -approximation for m = d = 2 and e e−1 ∼ 1.581977-approximation for other values of d, m. In a previous paper [4] we designed a PTAS (Polynomial Time Approximation Scheme) for that last problem. The PTAS is defined for the oblivious search model, but can be modified easily to work for the adaptive search model as well.…”

Section: Introductionmentioning

confidence: 99%

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The Conference Call Search Problem in Wireless Networks

Epstein

Levin

2006

Approximation and Online Algorithms

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Cellular telephony systems, where locations of mobile users are unknown at some times, are becoming more common. In such systems, mobile users are roaming in a zone and a user reports its location only if it leaves the zone entirely. The Conference Call Search problem (CCS) deals with tracking a set of mobile users in order to establish a call. To find a single roaming user, the system may need to search each cell where the user may be located. The goal is to identify the location of all users, within bounded time, satisfying some additional constraints on the search scheme. We consider cellular systems with n cells and m mobile users (cellular phones). The uncertain location of users is given by m probability distribution vectors. Whenever the system needs to find the users, it conducts a search operation lasting at most d rounds. A request for a single search step specifies a user and a cell. In this search step, the cell is asked whether the given user is located there. In each round the system may perform an arbitrary number of such requests. An integer number B ≥ 1 bounds the number of distinct requests per cell in every round. The bound d results from quality of service considerations whereas the bound B results from the wireless bandwidth allocated for signaling being scarce. Every search step consumes expensive wireless links, which motivates search techniques minimizing the expected number of requests thus reducing the total search costs. We distinguish between oblivious, semi-adaptive and adaptive search protocols. An oblivious search protocol decides on all requests in advance, and stops only when all users are found. A semi-adaptive search protocol decides on all the requests in advance, but it stops searching for a user once it is found. An adaptive search protocol stops searching for a user once it has been found (and its search strategy may depend on the subsets of users that were found in each previous round). We establish the difference between those three search models. We show that for oblivious "single query per cell" systems (B = 1), and a tight environment (d = m), it is NP-hard to compute an optimal solution (the case d = m = 2 was proven to be NP-hard already by Bar-Noy and Naor) and we develop a PTAS for these cases (for fixed values of d = m). However, we show that semi-adaptive systems allow polynomial time algorithms. This last result also shows that the case B = 1 and d = m = 2 is polynomially solvable also for adaptive search systems, answering an open question of Bar-Noy and Naor.

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Section: Usersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Conference Call Search Problem in Wireless Networks

Epstein

Levin

2006

Approximation and Online Algorithms

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“…Multicast search algorithm: Reference [15] designed an approximate optimal strategy of a polynomial time for multicast search problem, however, the algorithm only applied to the condition that the largest paging delay and the paging user number are fix. Reference [16] proposed a Sorted Round Robin (SRR) strategy.…”

Section: Introductionmentioning

confidence: 99%

A Multicast Search Scheme Based on Bipartite Graph Matching Model

Yao¹,

Zhang²,

Wang³

et al. 2015

IJSIP

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This paper proposes an efficient multicast search scheme based on bipartite graph matching model, aiming at one of the most important problems in the multicast service, how can the wireless network track and locate the mobile uses in the idle state, under the tight bandwidth and delay constraints,. By quantifying the location uncertainty of mobile users with Shannon's entropy, the scheme adopts the LZ78 compression algorithm to design location update scheme and predict the location probability, in order to reduce the cost of location update. The multicast search system need to guarantee the maximum total probability that each user resides at the assigned paging area, for the purpose of an optimal performance on both expected paging delay and paging cost. Therefore, the bigraph-based multicast paging scheme (BMPS) firstly builds the bipartite graph model of multicast search problem, through converting the location probability into weight of the edge. BMPS decides the optimal allocation between the mobile users and location areas, which is mainly achieved by the maximum weight perfect matching in bipartite graph, while modifying the weights dynamically. Simulation results show that BMPS yields a low search delay as well as a low search cost, and reduces the impact of user collision.

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