Anil M. Shende

Channel Assignment for Wireless Networks Modelled as d-Dimensional Square Grids

In this paper, we study the problem of channel assignment for wireless networks modelled as d-dimensional grids. In particular, for d-dimensional square grids, we present optimal assignments that achieve a channel separation of 2 for adjacent stations where the reuse distance is 3 or 4. We also introduce the notion of a colouring schema for d- dimensional square grids, and present an algorithm that assigns colours to the vertices of the grid satisfying the schema constraints.

Lattice computers for approximating Euclidean space

In the context of mesh-like, parallel processing computers for (i) approximating continuous space and (ii) <italic>analog</italic> simulation of the motion of objects and waves in continuous space, the present paper is concerned with <italic>which</italic> mesh-like interconnection of processors might be particularly suitable for the task and why. Processor interconnection schemes based on nearest neighbor connections in geometric lattices are presented along with motivation. Then two major threads are exploded regarding which lattices would be good: the <italic>regular lattices</italic>, for their symmetry and other properties in common with continuous space, and the well-known <italic>root lattices</italic>, for being, in a sense, the lattices required for physically natural basic algorithms for motion. The main theorem of the present paper implies that <italic>the</italic >well-known lattice A<italic><subscrpt>n</subscrpt></italic> is the regular lattice having the maximum number of nearest neighbors among the <italic>n</italic>-dimensional regular lattices. It is noted that the only <italic>n</italic>-dimensional lattices that are both regular and root are A<italic><subscrpt>n</subscrpt></italic> and Z<italic><supscrpt>n</supscrpt></italic> (Z<italic><supscrpt>n</supscrpt></italic> is the lattice of <italic>n</italic>-cubes. The remainder of the paper specifies other desirable properties of A<italic><subscrpt>n</subscprt</italic> including other ways it is superior to Z<italic><supscrpt>n</supscrpt></italic> for our purposes.

A characterisation of optimal channel assignments for cellular and square grid wireless networks

In this paper we first present a uniformity property that characterises optimal channel assignments for networks arranged as cellular or square grids. Then, we present optimal channel assignments for cellular and square grids; these assignments exhibit a high value for δ1 – the separation between channels assigned to adjacent stations. We prove an upper bound on δ1 for such optimal channel assignments. This upper bound is greater than the value of δ1 exhibited by our assignments. Based on empirical evidence, we conjecture that the value our assignments exhibit is a tight upper bound on δ1.

A characterization of root lattices

Abstract In this note we show that root lattices are all and only those lattices in which the set of minimal length vectors equals the set of relevant vectors.

A characterisation of optimal channel assignments for wireless networks modelled as cellular and square grids

In this paper we first present a uniformity property that characterises optimal channel assignments for networks arranged as cellular or square grids. Then, we present optimal channel assignments for cellular and square grids; these assignments exhibit a high value for /spl delta//sub 1/ - the separation between channels assigned to adjacent stations. Based on empirical evidence, we conjecture that the value our assignments exhibit is an upper bound on /spl delta//sub 1/.

Representing the Spatial/Kinematic Domain and Lattice Computers

An approach to analogical representation for objects and their motions in space is proposed.

Wireless ad hoc lattice computers (WAdL)

We propose an architecture to harness the comparatively low computational power of geographically concentrated mobile devices (such as in a wireless ad hoc network, especially a sensor network) to build a wireless ad hoc lattice computer (WAdL). The primary contribution of the WAdL design is the ability to maintain, despite the mobility of the participating devices, a virtual lattice where the devices represent lattice points. WAdL is a cellular automaton-like architecture designed to carry out simulations of the unfolding of physical phenomena (e.g., fluid flow, system of moving, interacting objects, etc.) in the bounded region of Euclidean space represented by the underlying virtual lattice of WAdL. We present the design and algorithms of the WAdL architecture, and demonstrate its use with an example application (lift and drag on an airplane wing in flight) implemented on a simulated WAdL environment. We also discuss current issues and future directions of work on the WAdL architecture.

Channel assignment in honeycomb networks

The honeycomb grid is a network topology based on the hexagonal plane tessellation, which is convenient to model the regular placement on the plane of the base stations of wireless networks. For an efficient use of the radio spectrum in such networks, channels have to be assigned to the base stations so as to avoid interferences. Such a problem can be modeled as a suitable coloring problem. Precisely, given an integer t and a honeycomb grid G=(V,E), an L(1 t )-coloring of G is a function f from the vertex set V to a set of nonnegative integers such that |f(u) − f(v)| ≥ 1, if the distance between the vertices u and v is at most t. This paper presents efficient algorithms for finding optimal L(1 t )-colorings of honeycomb grids.

Learning-theoretic perspectives of acceptable numberings

A class of recursive functionsC islimiting standardizable, in a programming system φ, iff there is an effective procedure which, given any φ-program (in the φ-system), synthesizes in the limit acanonical φ-program which is equivalent to the former. It can arguably be expected that notions similar to the above one would be relevant toGold-style function learning, which features, among other things, the effective limiting synthesis of programs for input recursive functions. Many learning classes have been characterized in terms of variants of the above notion. In this paper, we focus on the limiting standardizability of the entire class of recursive functions inEffective programming systems. To start with, we prove the independence of this notionvis-à-vis finitary recursion theorems. Secondly, we show that this motion does not entail acceptability, in the spirit of the results of Case, Riccardi and Royer on characterizations of the samevis-à-vis programming language control structures.

Spatial/kinematic domain and lattice computers

Abstract An approach to analogical representation for objects and their motions in space is proposed. This approach involves lattice computer architectures and associated algorithms and is shown to be abstracted from the behaviour of human beings mentally solving spatial/kinematic puzzles. There is also discussion of where in this approach the modelling of human cognition leaves off and the engineering begins. The possible relevance of the approach to a number of issues in artificial intelligence is discussed. These issues include efficiency of sentential versus analogical representations, common sense reasoning, update propagation, learning performance tasks, diagrammatic representations, spatial reasoning, metaphor, human categorization, and pattern recognition. Lastly there is a discussion of the somewhat related approach involving cellular automata applied to computational physics.