On the Displacement for Covering a d−d-dimensional Cube with Randomly Placed Sensors

Consider $n$ sensors placed randomly and independently with the uniform distribution in a $d-$dimensional unit cube ($d\ge 2$). The sensors have identical sensing range equal to $r$, for some $r >0$. We are interested in moving the sensors from their initial positions to new positions so as to ensure that the $d-$dimensional unit cube is completely covered, i.e., every point in the $d-$dimensional cube is within the range of a sensor. If the $i$-th sensor is displaced a distance $d_i$, what is a displacement of minimum cost? As cost measure for the displacement of the team of sensors we consider the $a$-total movement defined as the sum $M_a:= \sum_{i=1}^n d_i^a$, for some constant $a>0$. We assume that $r$ and $n$ are chosen so as to allow full coverage of the $d-$dimensional unit cube and $a > 0$. The main contribution of the paper is to show the existence of a tradeoff between the $d-$dimensional cube, sensing radius and $a$-total movement. The main results can be summarized as follows for the case of the $d-$dimensional cube. If the $d-$dimensional cube sensing radius is $\frac{1}{2n^{1/d}}$ and $n=m^d$, for some $m\in N$, then we present an algorithm that uses $O\left(n^{1-\frac{a}{2d}}\right)$ total expected movement (see Algorithm 2 and Theorem 5). If the $d-$dimensional cube sensing radius is greater than $\frac{3^{3/d}}{(3^{1/d}-1)(3^{1/d}-1)}\frac{1}{2n^{1/d}}$ and $n$ is a natural number then the total expected movement is $O\left(n^{1-\frac{a}{2d}}\left(\frac{\ln n}{n}\right)^{\frac{a}{2d}}\right)$ (see Algorithm 3 and Theorem 7). In addition, we simulate Algorithm 2 and discuss the results of our simulations

Computing Majority with Triple Queries

Consider a bin containing $n$ balls colored with two colors. In a $k$-query, $k$ balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the balls in this $k$-tuple; however, the oracle never reveals the colors of the individual balls. Following a number of queries the questioner is said to determine the majority color if it can output a ball of the majority color if it exists, and can prove that there is no majority if it does not exist. We investigate two computation models (depending on the type of replies being allowed). We give algorithms to compute the minimum number of 3-queries which are needed so that the questioner can determine the majority color and provide tight and almost tight upper and lower bounds on the number of queries needed in each case.Comment: 22 pages, 1 figure, conference version to appear in proceedings of the 17th Annual International Computing and Combinatorics Conference (COCOON 2011

Evaluation of Anonymized ONS Queries

Electronic Product Code (EPC) is the basis of a pervasive infrastructure for the automatic identification of objects on supply chain applications (e.g., pharmaceutical or military applications). This infrastructure relies on the use of the (1) Radio Frequency Identification (RFID) technology to tag objects in motion and (2) distributed services providing information about objects via the Internet. A lookup service, called the Object Name Service (ONS) and based on the use of the Domain Name System (DNS), can be publicly accessed by EPC applications looking for information associated with tagged objects. Privacy issues may affect corporate infrastructures based on EPC technologies if their lookup service is not properly protected. A possible solution to mitigate these issues is the use of online anonymity. We present an evaluation experiment that compares the of use of Tor (The second generation Onion Router) on a global ONS/DNS setup, with respect to benefits, limitations, and latency.Comment: 14 page