Abstract: We propose a MAC protocol for mobile ad hoc networks that
uses power control for the RTS/CTS and DATA frame
transmissions in order to improve energy and capacity
utilization efficiency. Unlike IEEE 802.11, in our scheme the
RTS frames are not sent using the maximum transmission
power to silence neighbouring nodes, and the CTS frames do
not silence all receiving nodes to the same degree. In contrast,
the transmission power of the RTS frames follows a slow
start principle, while the CTS frames, which are sent at
maximum transmission power, prevent the neighbouring
nodes from transmitting their DATA frames with power more
than a computed threshold, while allowing them to transmit at
power levels less than that threshold. This is done by
including in the RTS and the CTS frames additional
information, such as the power of the transmissions, and the
interference tolerance of the nodes. Moreover the DATA
frames are sent at the minimum required transmission power
increased by a small margin to ensure connectivity with the
intended receiver, so as to cause minimal interference to
neighbouring nodes and allow for future interference to be
added to the receiver of the DATA frames. The power to be
used by the transmitter is computed by the recipient of the
RTS frame and is included in the CTS frame. It is expected
that a network with such a power management scheme would
achieve a better throughput performance and more power
savings than a network without such a scheme.

Abstract: We propose a MAC protocol for mobile ad hoc networks that
uses power control for the RTS/CTS and DATA frame
transmissions in order to improve energy and capacity
utilization efficiency. Unlike IEEE 802.11, in our scheme the
RTS frames are not sent using the maximum transmission
power to silence neighbouring nodes, and the CTS frames do
not silence all receiving nodes to the same degree. In contrast,
the transmission power of the RTS frames follows a slow
start principle, while the CTS frames, which are sent at
maximum transmission power, prevent the neighbouring
nodes from transmitting their DATA frames with power more
than a computed threshold, while allowing them to transmit at
power levels less than that threshold. This is done by
including in the RTS and the CTS frames additional
information, such as the power of the transmissions, and the
interference tolerance of the nodes. Moreover the DATA
frames are sent at the minimum required transmission power
increased by a small margin to ensure connectivity with the
intended receiver, so as to cause minimal interference to
neighbouring nodes and allow for future interference to be
added to the receiver of the DATA frames. The power to be
used by the transmitter is computed by the recipient of the
RTS frame and is included in the CTS frame. It is expected
that a network with such a power management scheme would
achieve a better throughput performance and more power
savings than a network without such a scheme.

Abstract: We study the fundamental naming and counting problems in networks that are anonymous, unknown, and possibly dynamic. Network dynamicity is modeled by the 1-interval connectivity model [KLO10]. We first prove that on static networks with broadcast counting is impossible to solve without a leader and that naming is impossible to solve even with a leader and even if nodes know n. These impossibilities carry over to dynamic networks as well. With a leader we solve counting in linear time. Then we focus on dynamic networks with broadcast. We show that if nodes know an upper bound on the maximum degree that will ever appear then they can obtain an upper bound on n. Finally, we replace broadcast with one-to-each, in which a node may send a different message to each of its neighbors. This variation is then proved to be computationally equivalent to a full-knowledge model with unique names.

Abstract: In this work, we study the propagation of influence and computation in dynamic networks that are possibly disconnected at every instant. We focus on a synchronous message passing communication model with broadcast and bidirectional links. To allow for bounded end-to-end communication we propose a set of minimal temporal connectivity conditions that bound from the above the time it takes for information to make progress in the network. We show that even in dynamic networks that are disconnected at every instant information may spread as fast as in networks that are connected at every instant. Further, we investigate termination criteria when the nodes know some upper bound on each of the temporal connectivity conditions. We exploit our termination criteria to provide efficient protocols (optimal in some cases) that solve the fundamental counting and all-to-all token dissemination (or gossip) problems. Finally, we show that any protocol that is correct in instantaneous connectivity networks can be adapted to work in temporally connected networks.

Abstract: In this work, we study the propagation of influence and computation in dynamic distributed computing systems that are possibly disconnected at every instant. We focus on a synchronous message-passing communication model with broadcast and bidirectional links. Our network dynamicity assumption is a worst-case dynamicity controlled by an adversary scheduler, which has received much attention recently. We replace the usual (in worst-case dynamic networks) assumption that the network is connected at every instant by minimal temporal connectivity conditions. Our conditions only require that another causal influence occurs within every time window of some given length. Based on this basic idea, we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate termination criteria in networks in which an upper bound on any of these metrics is known. We exploit our termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental counting and all-to-all token dissemination (or gossip) problems.

Abstract: The problem of communication among mobile nodes is one of the most fundamental problems in ad hoc mobile networks and is at the core of many algorithms, such as for counting the number of nodes, electing a leader, data processing etc. For an exposition of several important problems in ad hoc mobile networks. The work of Chatzigiannakis, Nikoletseas and Spirakis focuses on wireless mobile networks that are subject to highly dynamic structural changes created by mobility, channel fluctuations and device failures. These changes affect topological connectivity, occur with high frequency and may not be predictable in advance. Therefore, the environment where the nodes move (in three-dimensional space with possible obstacles) as well as the motion that the nodes perform are \textit{input} to any distributed algorithm.

Abstract: We study the problem of maintaining connectivity in a wireless
network where the network nodes are equipped with
directional antennas. Nodes correspond to points on the
plane and each uses a directional antenna modeled by a sector
with a given angle and radius. The connectivity problem
is to decide whether or not it is possible to orient the antennas
so that the directed graph induced by the node transmissions
is strongly connected. We present algorithms for
simple polynomial-time-solvable cases of the problem, show
that the problem is NP-complete in the 2-dimensional case
when the sector angle is small, and present algorithms that
approximate the minimum radius to achieve connectivity for
sectors with a given angle. We also discuss several extensions
to related problems. To the best of our knowledge, the
problem has not been studied before in the literature.

Abstract: In this chapter, our focus is on computational network analysis from a theoretical point of view. In particular, we study the \emph{propagation of influence and computation in dynamic distributed computing systems}. We focus on a \emph{synchronous message passing} communication model with bidirectional links. Our network dynamicity assumption is a \emph{worst-case dynamicity} controlled by an adversary scheduler, which has received much attention recently. We first study the fundamental \emph{naming} and \emph{counting} problems (and some variations) in
networks that are \emph{anonymous}, \emph{unknown}, and possibly dynamic. Network dynamicity is modeled here by the \emph{1-interval connectivity model}, in which communication is synchronous and a (worst-case) adversary
chooses the edges of every round subject to the condition that each instance is connected. We then replace this quite strong assumption by minimal \emph{temporal connectivity} conditions. These conditions only require that \emph{another causal influence occurs within every time-window of some given length}. Based on this basic idea we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate \emph{termination criteria} in networks in which an upper bound on any of these metrics is known. We exploit these termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental \emph{counting} and \emph{all-to-all token dissemination} (or \emph{gossip}) problems. Finally, we propose another model of worst-case temporal connectivity, called \emph{local
communication windows}, that assumes a fixed underlying communication network and restricts the adversary to allow communication between local neighborhoods in every time-window of some fixed length. We prove some basic properties and provide a protocol for counting in this model.

Abstract: We consider a synchronous distributed system with n processes that communicate through a dynamic network guaranteeing 1-interval connectivity i.e., the network topology graph might change at each interval while keeping the graph connected at any time. The processes belonging to the distributed system are identified through a set of labels L = {l1 , l2 . . . , lk } (with 1 ≤ k < n). In this challenging system model, the paper addresses the following problem: ”counting the number of processes with the same label”. We provide a distributed algorithm that is able solve the problem based on the notion of energy transfer. Each process owns a fixed energy charge, and tries to discharge itself exchanging, at each round, at most half of its charge with neighbors. The paper also discusses when such counting is possible in the presence of failures. Counting processes with the same label in dynamic networks with homonyms is of great importance because it is as difficult as computing generic aggregating functions.

Abstract: In this work we investigate the problem of communication among mobile hosts, one of the most fundamental problems in ad-hoc mobile networks that is at the core of many algorithms. Our work investigates the extreme case of total absence of any fixed network backbone or centralized administration, instantly forming networks based only on mobile hosts with wireless communication capabilities, where topological connectivity is subject to frequent, unpredictable change.
For such dynamically changing networks we propose a set of protocols which exploit the coordinated (by the protocol) motion of a small part of the network in order to manage network operations. We show that such protocols can be designed to work correctly and efficiently for communication by avoiding message flooding. Our protocols manage to establish communication between any pair of mobile hosts in small, a-priori guaranteed expected time bounds. Our results exploit and further develop some fundamental properties of random walks in finite graph.
Apart from studying the general case, we identify two practical and interesting cases of ad-hoc mobile networks: a) hierarchical ad-hoc networks, b) highly changing ad-hoc networks, for which we propose protocols that efficiently deal with the problem of basic communication.
We have conducted a set of extensive experiments, comprised of thousands of mobile hosts in order to validate the theoretical results and show that our protocols achieve very efficient communication under different scenaria.

Abstract: An ad hoc mobile network is a collection of mobile hosts, with wireless communication capabilities, forming a temporary network without the aid of any established fixed infrastructure. In such networks, topological connectivity is subject to frequent, unpredictable change. Our work focuses on networks with high rate of such changes to connectivity. For such dynamically changing networks we propose protocols which exploit the co-ordinated (by the protocol) motion of a small part of the network. We show that such protocols can be designed to work correctly and efficiently even in the case of arbitrary (but not malicious) movements of the hosts not affected by the protocol. We also propose a methodology for the analysis of the expected behavior of protocols for such networks, based on the assumption that mobile hosts (those whose motion is not guided by the protocol) conduct concurrent random walks in their motion space. In particular, our work examines the fundamental problem of communication and proposes distributed algorithms for it. We provide rigorous proofs of their correctness, and also give performance analyses by combinatorial tools. Finally, we have evaluated these protocols by experimental means.

Abstract: An ad hoc mobile network is a collection of mobile hosts, with wireless communication capabilities, forming a temporary network without the aid of any established fixed infrastructure. In such networks, topological connectivity is subject to frequent, unpredictable change. Our work focuses on networks with high rate of such changes to connectivity. For such dynamically changing networks we propose protocols which exploit the co-ordinated (by the protocol) motion of a small part of the network. We show that such protocols can be designed to work correctly and efficiently even in the case of arbitrary (but not malicious) movements of the hosts not affected by the protocol. We also propose a methodology for the analysis of the expected behavior of protocols for such networks, based on the assumption that mobile hosts (those whose motion is not guided by the protocol) conduct concurrent random walks in their motion space. In particular, our work examines the fundamental problem of communication and proposes distributed algorithms for it. We provide rigorous proofs of their correctness, and also give performance analyses by combinatorial tools. Finally, we have evaluated these protocols by experimental means.

Abstract: Through recent technology advances in the eld 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 rst provide a formal denition of the charging
dispatch decision problem and prove its computational
hardness. We then investigate how to optimize the tradeo
s of several critical aspects of the charging process such
as a) the trajectory of the charger, b) the dierent 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 ndings demonstrate
signicant performance gains, both with respect to the no
charger case as well as the dierent charging alternatives; in
particular, the performance improvements include the network
lifetime, as well as connectivity, coverage and energy
balance properties.

Abstract: The energy balance property (i.e., all nodes having the same energy throughout the network evolution) contributes significantly (along with energy efficiency) to the maximization of the network lifespan and network connectivity. The problem of achieving energy balanced propagation is well studied in static networks, as it has attracted a lot of research attention.
Recent technological advances have enabled sensor devices to be attached to mobile entities of our every day life (e.g. smart-phones, cars, PDAs etc), thus introducing the formation of highly mobile sensor networks.
Inspired by the aforementioned applications, this work is (to the best of our knowledge) the first studying the energy balance property in wireless networks where the nodes are highly and dynamically mobile. In particular, in this paper we propose a new diverse mobility model which is easily parameterized and we also present a new protocol which tries to adaptively exploit the inherent node mobility in order to achieve energy balance in the network in an efficient way.

Abstract: We investigate important combinatorial and algorithmic properties of $G_{n, m, p}$ random intersection graphs. In particular, we prove that with high probability (a) random intersection graphs are expanders, (b) random walks on such graphs are ``rapidly mixing" (in particular they mix in logarithmic time) and (c) the cover time of random walks on such graphs is optimal (i.e. it is $\Theta(n \log{n})$). All results are proved for $p$ very close to the connectivity threshold and for the interesting, non-trivial range where random intersection graphs differ from classical $G_{n, p}$ random graphs.

Abstract: Dynamic graph algorithms have been extensively studied in the last two
decades due to their wide applicabilityin manycon texts. Recently, several
implementations and experimental studies have been conducted investigating
the practical merits of fundamental techniques and algorithms. In most
cases, these algorithms required sophisticated engineering and fine-tuning
to be turned into efficient implementations. In this paper, we surveysev -
eral implementations along with their experimental studies for dynamic
problems on undirected and directed graphs. The former case includes
dynamic connectivity, dynamic minimum spanning trees, and the sparsification
technique. The latter case includes dynamic transitive closure and
dynamic shortest paths. We also discuss the design and implementation of
a software libraryfor dynamic graph algorithms.

Abstract: Wireless networks are nowadays widely used and constantly evolving; we are constantly surrounded by numerous such networks. A modern idea is to exploit this variety and aggregate all available connections together towards improving Internet connectivity. In this paper we present our design of a networking system that enables participating entities to connect with each other and share their possible broadband connections. Every connected entity will gain broadband connection access from the ones that have and share one, independently from how many connections are available and how fast they are. Our goal is to improve the broadband connections' utilization and aim towards fault tolerance on these connections. To this end, the system is built on top of a peer-to-peer network, where the participating entities share their connections according to various scheduling algorithms.

Abstract: In this book chapter we will consider key establishment protocols for wireless sensor networks.
Several protocols have been proposed in the literature for the establishment of a shared group key for wired networks.
The choice of a protocol depends whether the key is established by one of the participants (and then transported to the other(s)) or agreed among the participants, and on the underlying cryptographic mechanisms (symmetric or asymmetric). Clearly, the design of key establishment protocols for sensor networks must deal with different problems and challenges that do not exist in wired networks. To name a few, wireless links are particularly vulnerable to eavesdropping, and that sensor devices can be captured (and the secrets they contain can be compromised); in many upcoming wireless sensor networks, nodes cannot rely on the presence of an online trusted server (whereas most standardized authentication and key establishment protocols do rely on such a server).
In particular, we will consider five distributed group key establishment protocols. Each of these protocols applies a different algorithmic technique that makes it more suitable for (i) static sensor networks, (ii) sensor networks where nodes enter sleep mode (i.e. dynamic, with low rate of updates on the connectivity graph) and (iii) fully dynamic networks where nodes may even be mobile. On the other hand, the common factor for all five protocols is that they can be applied in dynamic groups (where members can be excluded or added) and provide forward and backward secrecy. All these protocols are based on the Diffie-Hellman key exchange algorithm and constitute natural extensions of it in the multiparty case.

Abstract: In this work, we study the fundamental naming and counting problems (and some variations) in networks that are anonymous, unknown, and possibly dynamic. In counting, nodes must determine the size of the network n and in naming they must end up with unique identities. By anonymous we mean that all nodes begin from identical states
apart possibly from a unique leader node and by unknown that nodes
have no a priori knowledge of the network (apart from some minimal
knowledge when necessary) including ignorance of n. Network dynamicity is modeled by the 1-interval connectivity model [KLO10], in which communication is synchronous and a (worst-case) adversary chooses the edges of every round subject to the condition that each instance is connected. We first focus on static networks with broadcast where we prove that, without a leader, counting is impossible to solve and that naming is impossible to solve even with a leader and even if nodes know n. These impossibilities carry over to dynamic networks as well. We also show that a unique leader suffices in order to solve counting in linear time.
Then we focus on dynamic networks with broadcast. We conjecture that
dynamicity renders nontrivial computation impossible. In view of this,
we let the nodes know an upper bound on the maximum degree that will
ever appear and show that in this case the nodes can obtain an upper
bound on n. Finally, we replace broadcast with one-to-each, in which a
node may send a different message to each of its neighbors. Interestingly,
this natural variation is proved to be computationally equivalent to a
full-knowledge model, in which unique names exist and the size of the
network is known.

Abstract: An ad-hoc mobile network is a collection of mobile hosts, with
wireless communication capabilities, forming a temporary network
without the aid of any established fixed infrastructure.
In such networks, topological connectivity is subject to frequent,
unpredictable change. Our work focuses on networks with high
rate of such changes to connectivity. For such dynamic changing
networks we propose protocols which exploit the co-ordinated
(by the protocol) motion of a small part of the network.
We show that such protocols can be designed to work
correctly and efficiently even in the case of arbitrary (but not
malicious) movements of the hosts not affected by the protocol.
We also propose a methodology for the analysis of the expected
behaviour of protocols for such networks, based on the assumption that mobile hosts (whose motion is not guided by
the protocol) conduct concurrent random walks in their
motion space.
Our work examines some fundamental problems such as pair-wise
communication, election of a leader and counting, and proposes
distributed algorithms for each of them. We provide their
proofs of correctness, and also give rigorous analysis by
combinatorial tools and also via experiments.

Abstract: In this work we address the issue of efficient processing of range queries in DHT-based P2P data networks. The novelty of the proposed approach lies on architectures, algorithms, and mechanisms for identifying and appropriately exploiting powerful nodes in such networks. The existence of such nodes has been well documented in the literature and plays a key role in the architecture of most successful real-world P2P applications. However, till now, this heterogeneity has not been taken into account when architecting solutions for complex query processing, especially in DHT networks. With this work we attempt to fill this gap for optimizing the processing of range queries. Significant performance improvements are achieved due to (i) ensuring a much smaller hop count performance for range queries, and (ii) avoiding the dangers and inefficiencies of relying for range query processing on weak nodes, with respect to processing, storage, and communication capacities, and with intermittent connectivity. We present detailed experimental results validating our performance claims.

Abstract: In this work we consider the problem of finding Hamilton Cycles in graphs derived from the uniform random intersection graphs model $G_{n, m, p}$. In particular, (a) for the case $m = n^{\alpha}, \alpha>1$ 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 $G_{n, k}$ graph (i.e. a graph chosen equiprobably form the space of all graphs with $k$ edges), (b) we give an \textbf{expected polynomial time} algorithm for the case $p = \textrm{constant}$ and $m \leq \alpha \sqrt{\frac{n}{\log{n}}}$ for some constant $\alpha$, and (c) we show that the greedy approach still works well even in the case $m = o(\frac{n}{\log{n}})$ and $p$ just above the connectivity threshold of $G_{n, m, p}$ (found in \cite{Singerphd}) by giving a greedy algorithm that finds a Hamilton cycle in those ranges of $m, p$ with high probability.

Abstract: In this work we consider temporal networks, i.e. networks defined by a labeling $\lambda$ assigning to each edge of an underlying graph G a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by $\lambda$ a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees.

Abstract: We explore the capability of a network of extremely limited computational entities to decide properties about itself or any of its subnetworks. We consider that the underlying network of the interacting entities (devices, agents, processes etc.) is modeled by an interaction graph that reflects the network’s connectivity. We examine the following two cases: First, we consider the case where the input graph is the whole interaction graph and second where it is some subgraph of the interaction graph given by some preprocessing on the network. In each case, we devise simple graph protocols that can decide properties of the input graph. The computational entities, that are called agents, are modeled as finite-state automata and run the same global graph protocol. Each protocol is a fixed size grammar, that is, its description is independent of the size (number of agents) of the network. This size is not known by the agents. We present two simple models (one for each case), the Graph Decision Mediated Population Protocol (GDMPP) and the Mediated Graph Protocol (MGP) models, similar to the Population Protocol model of Angluin et al., where each network link (edge of the interaction graph) is characterized by a state taken from a finite set. This state can be used and updated during each interaction between the corresponding agents. We provide some example protocols and some interesting properties for the two models concerning the computability of graph languages in various settings (disconnected input graphs, stabilizing input graphs). We show that the computational power within the family of all (at least) weakly-connected input graphs is fairly restricted. Finally, we give an exact characterization of the class of graph languages decidable by the MGP model in the case of complete interaction graphs: it is equal to the class of graph languages decidable by a nondeterministic Turing Machine of linear space that receives its input graph by its adjacency matrix representation.

Abstract: In this paper we examine spectral properties of random intersection graphs when the number of vertices is equal to the number of labels. We call this class symmetric random intersection graphs. We examine symmetric random intersection graphs when the probability that a vertex selects a label is close to the connectivity threshold $\tau_c$. In particular, we examine the size of the second eigenvalue of the transition matrix corresponding to the Markov Chain that describes a random walk on an instance of the symmetric random intersection graph $G_{n, n, p}$. We show that with high probability the second eigenvalue is upper bounded by some constant $\zeta < 1$.

Abstract: In this paper we examine spectral properties of random intersection graphs when the number
of vertices is equal to the number of labels. We call this class symmetric random intersection graphs.
We examine symmetric random intersection graphs when the probability that a vertex selects a label
is close to the connectivity threshold ¿c. In particular, we examine the size of the second eigenvalue of
the transition matrix corresponding to the Markov Chain that describes a random walk on an instance
of the symmetric random intersection graph Gn,n,p. We show that with high probability the second
eigenvalue is upper bounded by some constant ³ < 1.