Miriam Di Ianni

Efficient Algorithms for Low-Energy Bounded-Hop Broadcast in Ad-Hoc Wireless Networks

The paper studies the problem of computing a minimal energy cost range assignment in a ad-hoc wireless network which allows a station s to perform a broadcast operation in at most h hops. The general version of the problem (i.e., when transmission costs are arbitrary) is known to be log-APX hard even for h = 2. The current paper considers the well-studied real case in which n stations are located on the plane and the cost to transmit from station i to station j is proportional to the α-th power of the distance between station i and j, where α is any positive constant. A polynomial-time algorithm is presented for finding an optimal range assignment to perform a 2-hop broadcast from a given source station. The algorithm relies on dynamic programming and operates in (worst-case) time O(n 7 ). Then, a polynomial-time approximation scheme (PTAS) is provided for the above problem for any fixed h > 1. For fixed h > 1 and ∈ > 0, the PTAS has time complexity O(n μ ) where μ = O((α2 α h α /∈)α h ).

Minimum-Energy Broadcast and disk cover in grid wireless networks

The Minimum Energy Broadcast problem consists in finding the minimum-energy range assignment for a given set S of n stations of an ad hoc wireless network that allows a source station to perform broadcast operations over S We prove a nearly tight asymptotical bound on the optimal cost for the Minimum Energy Broadcast problem on square grids. We emphasize that finding tight bounds for this problem restriction is far to be easy: it involves the Gausss Circle problem and the Apollonian Circle Packing. We also derive near-tight bounds for the Bounded-Hop version of this problem. Our results imply that the best-known heuristic, the MST-based one, for the Minimum Energy Broadcast problem is far to achieve optimal solutions (even) on very regular, well-spread instances: its worst-case approximation ratio is about π and it yields

Parameterized Parallel Complexity

\Omega(\sqrt{n})

Divide and conquer is almost optimal for the bounded-hop MST problem on random euclidean instances

hops As a by product, we get nearly tight bounds for the Minimum Disk Cover problem and for its restriction in which the allowed disks must have non-constant radius Finally, we emphasize that our upper bounds are obtained via polynomial time constructions

Spatial node distribution of manhattan path based random waypoint mobility models with applications

We introduce a framework to study the parallel complexity of parameterized problems, and we propose some analogs of NC.

Approximation algorithms for routing and call scheduling in all-optical chains and rings

The d-Dim h-hops MST problem is defined as follows: Given a set S of points in the d-dimensional Euclidean space and s ∈ S, find a minimum-cost spanning tree for S rooted at s with height at most h. We investigate the problem for any constants h and d > 0. We prove the first non trivial lower bound on the solution cost for almost all Euclidean instances (i.e. the lower-bound holds with high probability). Then we introduce an easy-to-implement, very fast divide and conquer heuristic and we prove that its solution cost matches the lower bound.

Minimum length scheduling of precedence constrained messages in distributed systems

In this paper, we study the spatial node stationary distribution of two variations of the Random Waypoint (in short, RWP) mobility model. In particular, differently from the RWP mobility model, that connects source to destination points by straight lines, our models make use of Manhattan or (more realistically) Bezier paths. We provide analytical results for the spatial node stationary distribution for the two Manhattan based RWP mobility models and experimental evidence that the Bezier based models do not significantly differ from the Manhattan ones. This implies that Manhattan based RWP models can be considered a good approximation of the more realistic Bezier ones. As a case study, we exploit our results about one of the two Manhattan based RWP models to derive an upper bound on the transmission range of the nodes of a MANET, moving according to this model, that with high probability guarantees the connectivity of the communication graph.

Acyclic orientations for deadlock prevention in interconnection networks

We study the problem of routing and scheduling requests of limited durations in an all-optical network. The task is servicing the requests, assigning each of them a starting time and a wavelength, with restrictions on the number of available wavelengths. The goal is minimizing the overall time needed to serve all requests. We propose constant approximation algorithms for both ring and chain networks. In doing this, we also propose a polynomial-time approximation scheme for the problem of routing weighted calls on a directed ring with minimum load.

Wormhole Deadlock Prediction

In a multiprocessor system, collisions occur because of simultaneous transmissions or receptions of two or more messages through the same port: messages are corrupted and must be retransmitted. Collisions can be avoided only by a proper scheduling of the messages. In this paper, minimum length schedulings of a set of communication requests subject to precedence constraints are studied. In particular, we first prove some complexity results and then we present some fast heuristics, assessing their average performance by means of computer simulation. The experimental results show that the heuristics perform quite well, and their expected values are very close to the average optimum.

Interval Routing & Layered Cross Product: Compact Routing Schemes for Butterflies, Mesh of Trees and Fat Trees

Cumene is prepared by alkylation of benzene with propylene in the presence of a solid phosphoric acid catalyst in a continuous process by delivering liquid benzene and liquid propylene in a molar ratio lower than 6:1, to a liquid reaction medium consisting essentially of benzene and cumene and containing the catalyst, while maintaining the temperature and composition of said medium substantially uniform in each point, operating at 170 DEG -280 DEG C. and in the liquid phase, and with a contact time higher than about 0.4 hours, expressed as the ratio between volume of catalyst and hourly volume of reagents fed in.