A Unified Semantics Space Model
Juan Ye, Lorcan Coyle, Simon Dobson, and Paddy Nixon
System Research Group, School of Computer Science and Informatics,
UCD, Dublin, Ireland
juan.ye@ucd.ie
Abstract. Location-aware systems provide customised services or applications
according to users’ locations. While much research has been carried out in de-
veloping models to represent location information and spatial relationships, it is
usually limited to modelling simple environments (cf. [13,19,3]). This paper pro-
poses a unified space model for more complex environments (e.g., city plan or
forest). This space model provides a flexible, expressive, and powerful spatial
representation. It also proposes a new data structure – an integrated lattice and
graph model – to express comprehensive spatial relationships. This structure not
only provides multiple graphs at different abstraction levels, but it also collapses
the whole map into smaller local graphs. This mechanism is beneficial in reducing
the complexity of creating and maintaining a map and improving the efficiency
of path finding algorithms.
1 Introduction
The development of location-aware systems has become commonplace recently. This
was encouraged by the availability of numerous available location sensing devices [11]
and by a popular demand for location-aware applications. A huge number of location
models have been developed – however most of them tend to either service particular
sensing abilities or application requirements.
Consider a complex real-world environment, such as a city or forest. It can be par-
titioned through multiple hierarchies (e.g., postcode areas, districts or compass direc-
tions) and involve a huge number of places (e.g., hundreds of streets or thousands of
buildings). In this environment, it may be necessary to describe the location of a certain
entity in various ways depending on the available location sensors. Most of existing
space models only provide traditional types of spatial representations, such as symbolic
and geometric representations. Especially some of these models support a single coor-
dinate reference system, because they only have one or two precise sensors that provide
location data in a coordinate format. As such, the ability of these models to flexibly
express location information is limited.
Our space model aims to support a powerful and expressive spatial representation. It
absorbs the best practices from existing models so as to support the traditional spatial
 This work is partially supported by Science Foundation Ireland under grant numbers
05/RFP/CMS0062 “Towards a semantics of pervasive computing” and 04/RPI/1544 “Secure
and predictable pervasive computing”.
J. Hightower, B. Schiele, and T. Strang (Eds.): LoCA 2007, LNCS 4718, pp. 103–120, 2007.
c© Springer-Verlag Berlin Heidelberg 2007

104 J. Ye et al.
representations, and makes improvements over them. This model supports multiple co-
ordinate systems from two perspectives: different global coordinate systems to support
different sensing technologies; and user-defined local coordinate systems to support
customised representations of environment instead of forcing all the spatial represen-
tations in a uniform coordinate system. Furthermore, this space model also supports
relative location representation [15]. Relative locations are necessary when the location
cannot be exactly specified or defined, or if the location is dynamic or moving. For
example, ‘a place 500m east of this building”, or “I am in the canteen of this train”.
Our approach can flexibly define a local reference system to describe these locations
in different directions by combining various kinds of spatial representations, while not
being limited to coordinates.
In complex environments it may also be necessary to construct a detailed map that
can provide a path to a destination for an entity among a large number of places (with
varied levels of granularity). There are two underlying models to organise spaces: hier-
archical and graph models, which represent containment and connectedness relation-
ships respectively. The typical approach to constructing a location map is to build
a single huge graph for the whole environment, while fixed at a certain granularity
(e.g., room-leveled spaces). This graph cannot be flexibly extended into coarser-grained
spaces (e.g., buildings or streets), or into finer-grained spaces (e.g., desks). Although
additional graphs may be built for these spaces, it is complicated to build a mapping
between them or coordinate them in applications. Most research experiments usually
take place in a building, so a single graph is easy to build and maintain. However, a sin-
gle graph for larger-scaled environments will take much effort and time to build and to
maintain its consistency and integrity. Also, existing models do not provide an approach
to collapse this graph so as to reduce the construction complexity.
In our space model, we propose a new data structure - a lattice integrated with graphs
to represent spatial relationships for complex environments. This space model applies
the lattice model to represent the containment relationship and applies the graph model
to represent the adjacency and connectedness relationships between spaces at the same
abstraction level. The integrated model builds a lattice model for all the spaces under a
certain partition approach. The graph models are embedded in the lattice model where
each node is associated with a graph whose vertices are the immediate sub spaces of
the node and whose edges are the adjacency and connectedness relations between these
vertices.
With this space model, system designers can build a single model to express all the
spatial relationships at once. They do not need to maintain separate hierarchy and graph
models and mappings between them. Furthermore, users can build graph models at
different abstraction levels whose hierarchies are managed in a lattice model. Even at
a certain abstraction level, the whole graph can be further divided into smaller graphs
that are associated with sibling nodes in the lattice. That is, each sibling node manages
a local graph that is part of the whole map. These local graphs can also be integrated to
form the whole map through a special space – a sensitive space – in the lattice model.
For a given set of spaces, a sensitive space is the largest of their common sub spaces,
whose detailed discussion will be in Section 3. This approach makes the graph model
easy to create and maintain. In addition, our space model improves the efficiency of path