Christoforos Raptopoulos

Efficient energy management in wireless rechargeable sensor networks

Through recent technology advances in the field of wireless energy transmission, Wireless Rechargeable Sensor Networks (WRSN) have emerged. In this new paradigm for WSNs a mobile entity called Mobile Charger (MC) traverses the network and replenishes the dissipated energy of sensors. In this work we first provide a formal definition of the charging dispatch decision problem and prove its computational hardness. We then investigate how to optimize the trade-offs of several critical aspects of the charging process such as a) the trajectory of the charger, b) the different charging policies and c) the impact of the ratio of the energy the MC may deliver to the sensors over the total available energy in the network. In the light of these optimizations, we then study the impact of the charging process to the network lifetime for three characteristic underlying routing protocols; a greedy protocol, a clustering protocol and an energy balancing protocol. Finally, we propose a Mobile Charging Protocol that locally adapts the circular trajectory of the MC to the energy dissipation rate of each sub-region of the network. We compare this protocol against several MC trajectories for all three routing families by a detailed experimental evaluation. The derived findings demonstrate significant performance gains, both with respect to the no charger case as well as the different charging alternatives; in particular, the performance improvements include the network lifetime, as well as connectivity, coverage and energy balance properties.

Determining Majority in Networks with Local Interactions and Very Small Local Memory

We study here the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types (states). The vertices may have a few additional possible states and can interact in pairs only if they share an edge. Any (population) protocol is required to stabilize in the initial majority, i.e. its output function must interpret the local state of each vertex so that each vertex outputs the initial majority type. We first provide a protocol with 4 states per vertex that always computes the initial majority value, under any fair scheduler. Under the uniform probabilistic scheduler of pairwise interactions, we prove that our protocol stabilizes in expected polynomial time for any network and is quite fast on the clique. As we prove, this protocol is optimal, in the sense that there does not exist any population protocol that always computes majority with fewer than 4 states per vertex. However this does not rule out the existence of a protocol with 3 states per vertex that is correct with high probability (whp). To this end, we examine an elegant and very natural majority protocol with 3 states per vertex, introduced in [2] where its performance has been analyzed for the clique graph. In particular, it determines the correct initial majority type in the clique very fast and whp under the uniform probabilistic scheduler. We study the performance of this protocol in arbitrary networks. We prove that, when the two initial states are put uniformly at random on the vertices, the protocol of [2] converges to the initial majority with probability higher than the probability of converging to the initial minority. In contrast, we present an infinite family of graphs, on which the protocol of [2] can fail, i.e. it can converge to the initial minority type whp, even when the difference between the initial majority and the initial minority is n − Θ(ln n). We also present another infinite family of graphs in which the protocol of [2] takes an expected exponential time to converge. These two negative results build upon a very positive result concerning the robustness of the protocol of [2] on the clique, namely that if the initial minority is at most \(\frac{n}{7}\), the protocol fails with exponentially small probability. Surprisingly, the resistance of the clique to failure causes the failure in general graphs. Our techniques use new domination and coupling arguments for suitably defined processes whose dynamics capture the antagonism between the states involved.

The existence and efficient construction of large independent sets in general random intersection graphs

We investigate the existence and efficient algorithmic construction of close to optimal independent sets in random models of intersection graphs. In particular, (a) we propose a new model for random intersection graphs (\(G_{n, m, \vec{p}}\)) which includes the model of [10] (the “uniform” random intersection graphs model) as an important special case. We also define an interesting variation of the model of random intersection graphs, similar in spirit to random regular graphs. (b) For this model we derive exact formulae for the mean and variance of the number of independent sets of size k (for any k) in the graph. (c) We then propose and analyse three algorithms for the efficient construction of large independent sets in this model. The first two are variations of the greedy technique while the third is a totally new algorithm. Our algorithms are analysed for the special case of uniform random intersection graphs.

Simple and efficient greedy algorithms for hamilton cycles in random intersection graphs

In this work we consider the problem of finding Hamilton Cycles in graphs derived from the uniform random intersection graphs model Gn, m, p. In particular, (a) for the case m=nα, α>1 we give a result that allows us to apply (with the same probability of success) any algorithm that finds a Hamilton cycle with high probability in a Gn, k graph (i.e. a graph chosen equiprobably form the space of all graphs with k edges), (b) we give an expected polynomial time algorithm for the case p = constant and

Determining majority in networks with local interactions and very small local memory

m \leq \alpha {\sqrt{{n}\over {{\rm log}n}}}

On the structure of equilibria in basic network formation

for some constant α, and (c) we show that the greedy approach still works well even in the case

Exploiting limited density information towards near-optimal energy balanced data propagation

m = o({{n}\over{{\rm log}n}})

Improving sensor network performance with wireless energy transfer

and p just above the connectivity threshold of Gn, m, p (found in [21]) by giving a greedy algorithm that finds a Hamilton cycle in those ranges of m, p with high probability.

Colouring Non-sparse Random Intersection Graphs

We study the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may later change into other types, out of a set of a few additional possible types, and can interact in pairs only if they share an edge. Any (population) protocol is required to stabilize in the initial majority. First we prove that there does not exist any population protocol that always computes majority in any interaction graph by using at most 3 types per vertex. However this does not rule out the existence of a protocol with 3 types per vertex that is correct with high probability (whp). To this end, we examine an elegant and very natural majority protocol with 3 types per vertex, introduced in Angluin et al. (Distrib. Computing 21(2):87–102, 2008), whose performance has been analyzed for the clique graph. In particular, we study the performance of this protocol in arbitrary networks, under the probabilistic scheduler. We prove that, if the initial assignement of types to vertices is random, the protocol of Angluin et al. (Distrib. Computing 21(2):87–102, 2008) converges to the initial majority with probability higher than the probability of converging to the initial minority. In contrast, we show that the resistance of the protocol to failure when the underlying graph is a clique causes the failure of the protocol in general graphs.

On Some Combinatorial Properties of Random Intersection Graphs

We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by 2], in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural property of equilibrium graphs. We show how to use this property in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest k-vicinity (defined as the set of vertices within distance k from a vertex), for any k ? 1 and in terms of the number of edges, thus settling positively a conjecture of 2] in the cases of graphs of large k-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough.Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an n-vertex star as a spanning subgraph. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.