One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, the length of the communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented compactly by a graph whose size is comparable with the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model.

Location information is very useful in the design of sensor network infrastructures. In this paper, we study the anchor-free 2D localization problem by using local angle measurements in a sensor network. We prove that given a unit disk graph and the angles between adjacent edges, it is NP-hard to find a valid embedding in the plane such that neighboring nodes are within distance 1 from each other and non-neighboring nodes are at least distance 1 away. Despite the negative results, however, one can find a planar spanner of a unit disk graph by using only local angles. The planar spanner can be used to generate a set of virtual coordinates that enable efficient and local routing schemes such as geographical routing or approximate shortest path routing. We also proposed a practical anchor-free embedding scheme by solving a linear program. We show by simulation that not only does it give very good local embedding, i.e., neighboring nodes are close and non-neighboring nodes are far away, but it also gives a quite accurate global view such that geographical routing and approximate shortest path routing on the embedded graph are almost identical to those on the original (true) embedding. The embedding algorithm can be adapted to other models of wireless sensor networks and is robust to measurement noise.

Abstract-Memories whose storage cells transit irreversibly between states have been common since the start of the data storage technology. In recent years, flash memories and other non-volatile memories based on floating-gate cells have become a very important family of such memories. We model them by the Write Asymmetric Memory (WAM), a memory where each cell is in one of q states -state 0, 1, ***, q -1 -and can only transit from a lower state to a higher state. Data stored in a WAM can be rewritten by shifting the cells to higher states. Since the state transition is irreversible, the number of times of rewriting is limited. When multiple variables are stored in a WAM, we study codes, which we call floating codes, that maximize the total number of times the variables can be written and rewritten.In this paper, we present several families of floating codes that either are optimal, or approach optimality as the codes get longer. We also present bounds to the performance of general floating codes. The results show that floating codes can integrate the rewriting capabilities of different variables to a surprisingly high degree.

Abstract-Certain storage media such as flash memories use write-asymmetric, multi-level storage elements. In such media, data is stored in a multi-level memory cell the contents of which can only be increased, or reset. The reset operation is expensive and should be delayed as much as possible. Mathematically, we consider the problem of writing a binary sequence into writeasymmetric q-ary cells, while recording the last r bits written. We want to maximize t, the number of possible writes, before a reset is needed. We introduce the term Buffer Code, to describe the solution to this problem. A buffer code is a code that remembers the r most recent values of a variable. We present the construction of a single-cell (n -1) buffer code that can store a binary (1 = 2) variable with t = PL '? 1 J + r -2 and a universal upper bound to the number of rewrites that a single-cell buffer code can have: t < qL1 j r+ [log,{[(q-1) mod (lr-1)]+1}1. We also show a binary buffer code with arbitrary n, q, r, namely, the code uses n q-ary cells to remember the r most recent values of one binary variable.The code can rewrite the variable t = (q -1) (n -2r + 1) + r -1 times, which is asymptotically optimal in q and n. We then extend the code construction for the case r = 2, and obtain a code that can rewrite the variable t = (q-1) (n-2) + 1 times. When q = 2, the code is strictly optimal.

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Abstract-A constrained memory is a storage device whose elements change their states under some constraints. A typical example is flash memories, in which cell levels are easy to increase but hard to decrease. In a general rewriting model, the stored data changes with some pattern determined by the application. In a constrained memory, an appropriate representation is needed for the stored data to enable efficient rewriting.In this paper, we define the general rewriting problem using a graph model. This model generalizes many known rewriting models such as floating codes, WOM codes, buffer codes, etc. We present a novel rewriting scheme for the flash-memory model and prove it is asymptotically optimal in a wide range of scenarios.We further study randomization and probability distributions to data rewriting and study the expected performance. We present a randomized code for all rewriting sequences and a deterministic code for rewriting following any i.i.d, distribution. Both codes are shown to be optimal asymptotically.

Abstract-WOM (Write Once Memory) codes are codes for efficiently storing and updating data in a memory whose state transition is irreversible. Storage media that can be classified as WOM includes flash memories, optical disks and punch cards. Error-correcting WOM codes can correct errors besides its regular data updating capability. They are increasingly important for electronic memories using MLCs (multi-level cells), where the stored data are prone to errors. In this paper, we study error-correcting WOM codes that generalize the classic models. In particular, we study codes for jointly storing and updating multiple variables -instead of one variable -in WOMs with multi-level cells. The error-correcting codes we study here are also a natural extension of the recently proposedfoating codes [7].We analyze the performance of the generalized errorcorrecting WOM codes and present several bounds. The number of valid states for a code is an important measure of its complexity. We present three optimal codes for storing two binary variables in n q-ary cells, where n = 1, 2, 3, respectively. We prove that among all the codes with the minimum number of valid states, the three codes maximize the total number of times the variables can be updated.

Abstract-Predetermined fixed thresholds are commonly used in nonvolatile memories for reading binary sequences, but they usually result in significant asymmetric errors after a long duration, due to voltage or resistance drift. This motivates us to construct error-correcting schemes with dynamic reading thresholds, so that the asymmetric component of errors are minimized. In this paper, we discuss how to select dynamic reading thresholds without knowing cell level distributions, and present several error-correcting schemes. Analysis based on Gaussian noise models reveals that bit error probabilities can be significantly reduced by using dynamic thresholds instead of fixed thresholds, hence leading to a higher information rate.