20 research outputs found
Local Approximation Schemes for Ad Hoc and Sensor Networks
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs
Embedding of Virtual Network Requests over Static Wireless Multihop Networks
Network virtualization is a technology of running multiple heterogeneous
network architecture on a shared substrate network. One of the crucial
components in network virtualization is virtual network embedding, which
provides a way to allocate physical network resources (CPU and link bandwidth)
to virtual network requests. Despite significant research efforts on virtual
network embedding in wired and cellular networks, little attention has been
paid to that in wireless multi-hop networks, which is becoming more important
due to its rapid growth and the need to share these networks among different
business sectors and users. In this paper, we first study the root causes of
new challenges of virtual network embedding in wireless multi-hop networks, and
propose a new embedding algorithm that efficiently uses the resources of the
physical substrate network. We examine our algorithm's performance through
extensive simulations under various scenarios. Due to lack of competitive
algorithms, we compare the proposed algorithm to five other algorithms, mainly
borrowed from wired embedding or artificially made by us, partially with or
without the key algorithmic ideas to assess their impacts.Comment: 22 page
The Clique Problem in Intersection Graphs of Ellipses and Triangles
Intersection graphs of disks and of line segments, respectively, have been well studied, because of both practical applications and theoretically interesting properties of these graphs. Despite partial results, the complexity status of the Clique problem for these two graph classes is still open. Here, we consider the Clique problem for intersection graphs of ellipses, which, in a sense, interpolate between disks and line segments, and show that the problem is APX-hard in that case. Moreover, this holds even if for all ellipses, the ratio of the larger over the smaller radius is some prescribed number. Furthermore, the reduction immediately carries over to intersection graphs of triangles. To our knowledge, this is the first hardness result for the Clique problem in intersection graphs of convex objects with finite description complexity. We also describe a simple approximation algorithm for the case of ellipses for which the ratio of radii is bounde