9775694
Paging Mobile Users Efficiently and Optimally
A mobile user is roaming in a zone composed of N cells in a cellular network system. When a call to the mobile user arrives, the system pages the mobile user in these cells since it never reports its location unless it leaves the zone. The N cells are associated with a probability vector (p1, ...,pN) where pi is the probability that the mobile user resides in the ith cell and all the probabilities are independent. A delay constraint paging strategy must find the mobile user within D (1 les D les N) paging rounds; in each round a subset of the N cells is paged. The goal is to minimize the expected number of paged cells until the mobile user is found. Solutions based on dynamic programming that yield optimal strategies are known. The running time of the known implementations is Theta(N2D). Our first contribution is to improve the running time to Theta(ND) by proving that the dynamic programming recursive formulation satisfies the Monge property, permitting us to use various dynamic programming speedup techniques. A Theta(N) heuristic solution is also known. Our second contribution is a heuristic whose running time is Theta(N log D). Our heuristic outperforms the known heuristic while running faster for D << N. We compare the non-optimal heuristics with the optimal solution demonstrating the tradeoff between optimality and running time efficiency of various solutions.
15303871
When to Reap and When to Sow - Lowering Peak Usage with Realistic Batteries
In some energy markets, large clients are charged for both total energy usage and peak energy usage, which is based on the maximum single energy request over the billing period. The problem of minimizing peak charges was recently introduced as an online problem in [4], which gave optimally competitive algorithms. In this problem, a battery (previously assumed to be perfectly efficient) is used to store energy for later use. In this paper, we extend the problem to the more realistic setting of lossy batteries, which lose to conversion inefficiency a constant fraction of any amount charged (e.g. 33%). For this setting, we provide efficient and optimal offline algorithms as well as possibly competitive online algorithms. Second, we give factor-revealing LPs, which provide some quasi-empirical evidence for competitiveness. Finally, we evaluate these and other, heuristic algorithms on real and synthetic data.
16637089
Finding mobile data under delay constraints with searching costs
A token is hidden in one of several boxes and then the boxes are locked. The probability of placing the token in each of the boxes is known. A searcher is looking for the token by unlocking boxes where each box is associated with an unlocking cost. The searcher conducts its search in rounds and must find the token in a predetermined number of rounds. In each round, the searcher may unlock any set of locked boxes concurrently. The optimization goal is to minimize the expected cost of unlocking boxes until the token is found. The motivation and main application of this game is the task of paging a mobile user (token) who is roaming in a zone of cells (boxes) in a cellular network system. Here, the unlocking costs reflect cell congestions and the placing probabilities represent the likelihood of the user residing in particular cells. Another application is the task of finding some data (token) that may be known to one of the sensors (boxes) of a sensor network. Here, the unlocking costs reflect the energy consumption of querying sensors and the placing probabilities represent the likelihood of the data being found in particular sensors. In general, we call mobile data any entity that has to be searched for.
 The special case, in which all the boxes have equal unlocking costs has been well studied in recent years and several optimal polynomial time solutions exist. To the best of our knowledge, this paper is the first to study the general problem in which each box may be associated with a different unlocking cost. We first present three special interesting and important cases for which optimal polynomial time algorithms exist: (i) There is no a priori knowledge about the location of the token and therefore all the placing probabilities are the same. (ii) There are no delay constraints so in each round only one box is unlocked. (iii) The token is atypical in the sense that it is more likely to be placed in boxes whose unlocking cost is low. Next, we consider the case of a typical token for which the unlocking cost of any box is proportional to the probability of placing the token in this box. We show that computing the optimal strategy is strongly NP-Hard for any number of unlocking rounds, we provide a PTAS algorithm, and analyze a greedy solution. We propose a natural dynamic programming heuristic that unlocks the boxes in a non-increasing order of the ratio probability over cost. For two rounds, we prove that this strategy is a 1.143-approximation solution for an arbitrary token and a 1.108-approximation for a typical token and that both bounds are tight. For an arbitrary token, we provide a more complicated PTAS
14333699
Clock Domain Crossing Fault Model and Coverage Metric for Validation of SoC Design
Multiple asynchronous clock domains have been increasingly employed in System-on-Chip (SoC) designs for different I/O interfaces. Functional validation is one of the most expensive tasks in the SoC design process. Simulation on register transfer level (RTL) is still the most widely used method. It is important to quantitatively measure the validation confidence and progress for clock domain crossing (CDC) designs. In this paper, we propose an efficient method for definition of CDC coverage, which can be used in RTL simulation for a multi-clock domain SoC design. First, we develop a CDC fault model to present the actual effect of metastability. Second, we use a temporal data flow graph (TDFG) to propagate the CDC faults to observable variables. Finally, CDC coverage is defined based on the CDC faults and their observability. Our experiments on a commercial IP demonstrate that this method is useful to find CDC errors early in the design cycles.