Abstract: We study the problem of fast and energy-efficient data collection of sensory data using a mobile sink, in wireless sensor networks in which both the sensors and the sink move. Motivated by relevant applications, we focus on dynamic sensory mobility and heterogeneous sensor placement. Our approach basically suggests to exploit the sensor motion to adaptively propagate information based on local conditions (such as high placement concentrations), so that the sink gradually “learns” the network and accordingly optimizes its motion. Compared to relevant solutions in the state of the art (such as the blind randomwalk, biased walks, and even optimized deterministic sink mobility), our method significantly reduces latency (the improvement ranges from 40% for uniform placements, to 800% for heterogeneous ones), while also improving the success rate and keeping the energy dissipation at very satisfactory levels.

Abstract: In this paper, we consider the problem of energy balanced data propagation in wireless sensor networks and we generalise previous works by allowing realistic energy assignment. A new modelisation of the process of energy consumption as a randomwalk along with a new analysis are proposed. Two new algorithms are presented and analysed. The first one is easy to implement and fast to execute. However, it needs a priori assumptions on the process generating data to be propagated. The second algorithm overcomes this need by inferring information from the observation of the process. Furthermore, this algorithm is based on stochastic estimation methods and is adaptive to environmental changes. This represents an important contribution for propagating energy balanced data in wireless sensor netwoks due to their highly dynamic nature.

Abstract: In this paper we study the problem of basic communication
in ad-hoc mobile networks where the deployment area changes in a
highly dynamic way and is unknown. We call such networks
highly changing ad-hoc mobile networks.
For such networks we investigate an efficient communication protocol which extends
the idea (introduced in [WAE01,POMC01]) of exploiting the co-ordinated
motion of a small part of an ad-hoc mobile
network (the ``runners support") to achieve
very fast communication between any two mobile users of the network.
The basic idea of the new protocol presented here is, instead
of using a fixed sized support for the whole duration of the protocol,
to employ a support of some initial (small) size which
adapts (given some time which can be made fast enough) to the
actual levels of traffic and the
(unknown and possibly rapidly changing) network area by
changing its size in order to converge to an optimal size,
thus satisfying certain Quality of Service criteria.
We provide here some proofs of correctness and fault tolerance
of this adaptive approach and we also provide analytical results
using Markov Chains and randomwalk techniques to show that such
an adaptive approach is, for this class of ad-hoc mobile networks, significantly more efficient than a simple non-adaptive
implementation of the basic ``runners support" idea.

Abstract: We investigate the problem of communication in an ad-hoc mobile network, that is, we assume the extreme case of a total absense of any fixed network infrastructure (for example a case of rapid deployment of a set of mobile hosts in an unknown terrain). We propose, in such a case, that a small subset of the deployed hosts (which we call the support) should be used for network operations. However, the vast majority of the hosts are moving arbitrarily according to application needs.
We then provide a simple, correct and efficient protocol for communication that avoids message flooding. Our protocol manages to establish communication between any pair of mobile hosts in small, a-priori guaranteed expected time bounds even in the worst case of arbitrary motions of the hosts that not in the support (provided that they do not deliberately try to avoid the support). These time bounds, interestingly, do not depend, on the number of mobile hosts that do not belong in the support. They depend only on the size of the area of motions. Our protocol can be implemented in very efficient ways by exploiting knowledge of the space of motions or by adding more power to the hosts of the support.
Our results exploit and further develop some fundamental properties of randomwalks in finite graphs.

Abstract: We introduce a new model of
ad-hoc mobile networks, which we call hierarchical,
that are comprised of dense subnetworks of mobile
users (corresponding to highly populated
geographical areas, such as cities),
interconnected across access ports
by sparse but frequently used connections
(such as highways).
For such networks, we present
an efficient routing protocol which extends
the idea (introduced in WAE00) of exploiting the co-ordinated
motion of a small part of an ad-hoc mobile
network (the ``support'') to achieve
very fast communication between any two mobile users of the network.
The basic idea of the new protocol presented here is, instead
of using a unique (large) support for the whole network,
to employ a hierarchy of (small) supports (one for each city)
and also take advantage of the regular traffic
of mobile users across the interconnection highways to communicate
between cities.
We combine here theoretical analysis (average case estimations based on randomwalk properties) and experimental implementations (carried out using the LEDA platform) to claim and validate results showing that such a hierarchical routing approach is,
for this class of ad-hoc mobile networks, significantly more efficient than a simple extension of the
basic ``support'' idea presented in WAE00.

Abstract: We investigate basic communication protocols in ad-hoc mobile networks. We follow the semi-compulsory approach according to which a small part of the mobile users, the support , that moves in a predetermined way is used as an intermediate pool for receiving and delivering messages. Under this approach, we present a new semi-compulsory protocol called the runners in which the members of perform concurrent and continuous randomwalks and exchange any information given to them by senders when they meet. We also conduct a comparative experimental study of the runners protocol with another existing semi-compulsory protocol, called the snake, in which the members of move in a coordinated way and always remain pairwise adjacent. The experimental evaluation has been carried out in a new generic framework that we developed to implement protocols for mobile computing. Our experiments showed that for both protocols only a small support is required for efficient communication, and that the runners protocol outperforms the snake protocol in almost all types of inputs we considered.

Abstract: An ad-hoc mobile network is a collection of mobile hosts, with wireless communication capability, forming a temporary network without the aid of any established fixed infrastructure. In such a (dynamically changing) network it is not at all easy to avoid broadcasting (and flooding).
In this paper we propose, theoretically analyse and experimentally validate a new and efficient protocol for pairwise communication. The protocol exploits the co-ordinated motion of a small part of the network (i.e. it is a semi-compulsory protocol) in order to provide to various senders and receivers an efficient support for message passing. Our implementation platform is the LEDA system and we have tested the protocol for three classes of graphs (grids, random graphs and bipartite multi-stage graphs) each ing a different ?motion topology?.
Our theoretical analysis (based on properties of randomwalks) and our experimental measurements indicate that only a small fraction of the mobile stations are enough to be exploited by the support in order to achieve very fast communication between any pair of mobile stations.

Abstract: We introduce a new model of ad-hoc mobile networks,
which we call hierarchical, that are comprised of
dense subnetworks of mobile users (corresponding to highly
populated geographical areas), interconnected across access
ports by sparse but frequently used connections.
To implement communication in such a case, a possible
solution would be to install a very fast (yet limited) backbone
interconnecting such highly populated mobile user areas, while
employing a hierarchy of (small) supports (one for each lower level
site). This fast backbone provides a limited number of access
ports within these dense areas of mobile users.
We combine here theoretical analysis (average case estimations based on
randomwalk properties) to claim and validate
results showing that such a hierarchical routing approach is,
for this class of ad-hoc mobile networks, significantly
more efficient than a simple extension of the
basic ``support'' idea presented in [WAE00,DISC01].

Abstract: Consider k particles, 1 red and k–1 white, chasing each other on the nodes of a graph G. If the red one catches one of the white, it ldquoinfectsrdquo it with its color. The newly red particles are now available to infect more white ones. When is it the case that all white will become red? It turns out that this simple question is an instance of information propagation between randomwalks and has important applications to mobile computing where a set of mobile hosts acts as an intermediary for the spread of information.
In this paper we model this problem by k concurrent randomwalks, one corresponding to the red particle and k–1 to the white ones. The infection time Tk of infecting all the white particles with red color is then a random variable that depends on k, the initial position of the particles, the number of nodes and edges of the graph, as well as on the structure of the graph.
We easily get that an upper bound on the expected value of Tk is the worst case (over all initial positions) expected meeting time m* of two randomwalks multiplied by THgr (log k). We demonstrate that this is, indeed, a tight bound; i.e. there is a graph G (a special case of the ldquolollipoprdquo graph), a range of values k

Abstract: Randomwalks in wireless sensor networks can serve as fully
local, very simple strategies for sink motion that reduce energy dissipa-
tion a lot but increase the latency of data collection. To achieve satis-
factory energy-latency trade-offs the sink walks can be made adaptive,
depending on network parameters such as density and/or history of past
visits in each network region; but this increases the memory require-
ments. Towards better balances of memory/performance, we propose two
new randomwalks: the RandomWalk with Inertia and the Explore-and-
Go RandomWalk; we also introduce a new metric (Proximity Varia-
tion) that captures the different way each walk gets close to the network
nodes. We implement the new walks and experimentally compare them
to known ones. The simulation findings demonstrate that the new walk¢s
performance (cover time) gets close to the one of the (much stronger)
biased walk, while in some other respects (partial cover time, proximity
variation) they even outperform it. We note that the proposed walks
have been fine-tuned in the light of experimental findings.

Abstract: In this work we introduce two practical and interesting models of ad-hoc mobile networks: (a) hierarchical ad-hoc networks, comprised of dense subnetworks of mobile users interconnected by a very fast yet limited backbone infrastructure, (b) highly changing ad-hoc networks, where the deployment area changes in a highly dynamic way and is unknown to the protocol. In such networks, we study the problem of basic communication, i.e., sending messages from a sender node to a receiver node. For highly changing networks, we investigate an efficient communication protocol exploiting the coordinated motion of a small part of an ad-hoc mobile network (the ldquorunners supportrdquo) to achieve fast communication. This protocol instead of using a fixed sized support for the whole duration of the protocol, employs a support of some initial (small) size which adapts (given some time which can be made fast enough) to the actual levels of traffic and the (unknown and possibly rapidly changing) network area, by changing its size in order to converge to an optimal size, thus satisfying certain Quality of Service criteria. Using randomwalks theory, we show that such an adaptive approach is, for this class of ad-hoc mobile networks, significantly more efficient than a simple non-adaptive implementation of the basic ldquorunners supportrdquo idea, introduced in [9,10]. For hierarchical ad-hoc networks, we establish communication by using a ldquorunnersrdquo support in each lower level of the hierarchy (i.e., in each dense subnetwork), while the fast backbone provides interconnections at the upper level (i.e., between the various subnetworks). We analyze the time efficiency of this hierarchical approach. This analysis indicates that the hierarchical implementation of the support approach significantly outperforms a simple implementation of it in hierarchical ad-hoc networks. Finally, we discuss a possible combination of the two approaches above (the hierarchical and the adaptive ones) that can be useful in ad-hoc networks that are both hierarchical and highly changing. Indeed, in such cases the hierarchical nature of these networks further supports the possibility of adaptation.

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 randomwalks 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: When one engineers distributed algorithms, some special characteristics
arise that are different from conventional (sequential or parallel)
computing paradigms. These characteristics include: the need for either a
scalable real network environment or a platform supporting a simulated
distributed environment; the need to incorporate asynchrony, where arbitrarya
synchrony is hard, if not impossible, to implement; and the generation
of “difficult” input instances which is a particular challenge. In this
work, we identifys ome of the methodological issues required to address
the above characteristics in distributed algorithm engineering and illustrate
certain approaches to tackle them via case studies. Our discussion
begins byad dressing the need of a simulation environment and how asynchronyis
incorporated when experimenting with distributed algorithms.
We then proceed bys uggesting two methods for generating difficult input
instances for distributed experiments, namelya game-theoretic one and another
based on simulations of adversarial arguments or lower bound proofs.
We give examples of the experimental analysis of a pursuit-evasion protocol
and of a shared memorypro blem in order to demonstrate these ideas.
We then address a particularlyi nteresting case of conducting experiments
with algorithms for mobile computing and tackle the important issue of
motion of processes in this context. We discuss the two-tier principle as
well as a concurrent randomwalks approach on an explicit representation
of motions in ad-hoc mobile networks, which allow at least for averagecase
analysis and measurements and may give worst-case inputs in some
cases. Finally, we discuss a useful interplay between theory and practice
that arise in modeling attack propagation in networks.

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 randomwalks 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 randomwalks 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: In this thesis we investigate the problems of data routing and data collection in wireless sensor networks characterised by intense and higly diverse mobility. We propose a set of protocols that takes exploits the motion of the sensors in order to inform the sink about the network topology. We experimentally evaluate these protocolls in a wide range of topologies, including both homogeneous and heterogeneous ones.
We also investigate randomwalks as simple motion strategies for mobile sinks that perform data collection from static WSN's. We propose three new randomwalks that improve latency compared to already known ones, as well as a new metric called Proximity Variation. This metric captures the different way each randomwalks traverses the network area.

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) randomwalks on such graphs are ``rapidly mixing" (in particular they mix in logarithmic time) and (c) the cover time of randomwalks 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: Energy is a scarce resource in ad hoc wireless networks and it
is of paramount importance to use it e±ciently when establishing com-
munication patterns. In this work we study algorithms for computing
energy-e±cient multicast trees in ad hoc wireless networks. Such algo-
rithms either start with an empty solution which is gradually augmented
to a multicast tree (augmentation algorithms) or take as input an initial
multicast tree and `walk' on di®erent multicast trees for a ¯nite number
of steps until some acceptable decrease in energy consumption is achieved
(local search algorithms).
We mainly focus on augmentation algorithms and in particular we have
implemented a long list of existing such algorithms in the literature and
new ones. We experimentally compare all these algorithms on random
geometric instances of the problem and obtain results in terms of the
energy e±ciency of the solutions obtained. Additional results concerning
the running time of our implementations are also presented. We also ex-
plore how much the solutions obtained by augmentation algorithms can
be improved by local search algorithms. Our results show that one of our
new algorithms and its variations achieve the most energy-e±cient solu-
tions while being very fast. Our investigations shed some light to those
properties of geometric instances of the problem which make augmenta-
tion algorithms perform well.

Abstract: We study the problem of fast and energy-efficient
data collection of sensory data using a mobile sink, in wireless sensor networks in which both the sensors and the sink move. Motivated by relevant applications, we focus on dynamic sensory
mobility and heterogeneous sensor placement. Our approach basically suggests to exploit the sensor motion to adaptively propagate information based on local conditions (such as high placement concentrations), so that the sink gradually ”learns”
the network and accordingly optimizes its motion. Compared to relevant solutions in the state of the art (such as the blind randomwalk, biased walks, and even optimized deterministic sink mobility), our method significantly reduces latency (the improvement ranges from 40% for uniform placements, to 800% for heterogeneous ones), while also improving the success rate and keeping the energy dissipation at very satisfactory levels.

Abstract: Motivated by the problem of efficiently collecting data from
wireless sensor networks via a mobile sink, we present an accelerated
randomwalk on Random Geometric Graphs. Randomwalks in wireless sensor networks can serve as fully local,
very simple strategies for sink motion that significantly
reduce energy dissipation but introduce higher latency in the
data collection process. While in most cases randomwalks
are studied on graphs like Gn,p and Grid, we define and experimentally
evaluate our newly proposed randomwalk on
the Random Geometric Graphs model, that more accurately
abstracts spatial proximity in a wireless sensor network. We
call this new randomwalk the \~{a}-stretched randomwalk, and
compare it to two known randomwalks; its basic idea is
to favour visiting distant neighbours of the current node
towards reducing node overlap. We also define a new performance
metric called Proximity Cover Time which, along
with other metrics such as visit overlap statistics and proximity
variation, we use to evaluate the performance properties
and features of the various walks.

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 randomwalks 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: We investigate here the problem
of establishing communication in an ad-hoc
mobile network, that is, we assume the extreme case
of a total absence of any fixed network infrastructure
(for example a case of rapid deployment of a set of
mobile hosts in an unknown terrain). We propose, in
such a case, that a small
subset of the deployed hosts (which we call the support)
should be used to manage network operations.
However, the vast majority
of the hosts are moving arbitrarily according
to application needs.
We then provide a simple, correct and efficient protocol
for communication establishment
that avoids message flooding.
Our protocol manages to establish communication between
any pair of mobile hosts in small, a-priori
guaranteed time bounds even in the worst case of arbitrary motions of the hosts that do not belong to
the support (provided that they do not deliberately try
to avoid the support).
These time bounds, interestingly, do not depend,
on the number of mobile hosts that do not
belong in the support. They depend only on the size of the area
of motions.
Our protocol can be implemented
in very efficient ways by exploiting knowledge of the space of motions
or by adding more power to the hosts of the support.
Our results exploit and further develop some
fundamental properties of randomwalks in finite graphs.

Abstract: We consider the important problem of energy balanced data propagation in wireless sensor networks and we extend and generalize
previous works by allowing adaptive energy assignment. We consider the data gathering problem where data are generated by the sensors and
must be routed toward a unique sink. Sensors route data by either sending the data directly to the sink or in a multi-hop fashion by delivering
the data to a neighbouring sensor. Direct and neighbouring transmissions require different levels of energy consumption. Basically, the protocols balance the energy consumption among the sensors by computing the adequate ratios of direct and neighbouring transmissions. An abstract model of energy dissipation as a randomwalk is proposed, along with rigorous performance analysis techniques. Two efficient distributed algorithms are presented and analysed, by both rigorous means and simulation.
The first one is easy to implement and fast to execute. The protocol assumes that sensors know a-priori the rate of data they generate.
The sink collects and processes all these information in order to compute the relevant value of the protocol parameter. This value is transmitted
to the sensors which individually compute their optimal ratios of direct and neighbouring transmissions. The second protocol avoids the necessary a-priori knowledge of the data rate generated by sensors by inferring the relevant information from the observation of the data paths.
Furthermore, this algorithm is based on stochastic estimation methods and is adaptive to environmental changes.

Abstract: We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This represents a known upper bound on the cover time of a randomwalk. The cover-time service allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space log n with input commutativity, where n is the number of nodes in the network. We also give a log n-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.

Abstract: We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This is simply a known upper bound on the cover time of a randomwalk. This allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space logn with input commutativity, where n is the number of nodes in the network. We also give a logn-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.

Abstract: Consider k particles, 1 red and k-1 white, chasing each other on the nodes of a graph G. If the red one catches one of the white, it “infects” it with its color. The newly red particles are now available to infect more white ones. When is it the case that all white will become red? It turns out that this simple question is an instance of information propagation between randomwalks and has important applications to mobile computing where a set of mobile hosts acts as an intermediary for the spread of information.
In this paper we model this problem by k concurrent randomwalks, one corresponding to the red particle and k-1 to the white ones. The infection time Tk of infecting all the white particles with red color is then a random variable that depends on k, the initial position of the particles, the number of nodes and edges of the graph, as well as on the structure of the graph.
In this work we develop a set of probabilistic tools that we use to obtain upper bounds on the (worst case w.r.t. initial positions of particles) expected value of Tk for general graphs and important special cases. We easily get that an upper bound on the expected value of Tk is the worst case (over all initial positions) expected meeting time m* of two randomwalks multiplied by . We demonstrate that this is, indeed, a tight bound; i.e. there is a graph G (a special case of the “lollipop” graph), a range of values k

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 randomwalk 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 randomwalk 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.

Abstract: We study here dynamic antagonism in a fixed network, represented as a graph $G$ of $n$ vertices. In particular, we consider the case of $k \leq n$ particles walking randomly independently around the network. Each particle belongs to exactly one of two antagonistic species, none of which can give birth to children. When two particles meet, they are engaged in a (sometimes mortal) local fight. The outcome of the fight depends on the species to which the particles belong. Our problem is \emph{to predict} (i.e. to compute) the eventual chances of species survival. We prove here that this can indeed be done in \emph{expected polynomial time on the size of the network}, provided that the network is \emph{undirected}.

Abstract: Motivated by the problem of efficient sensor network data collection via a mobile sink, we present undergoing research in accelerated randomwalks on Random Geometric Graphs. We first propose a new type of randomwalk, called the {\'a}-stretched randomwalk, and compare it to three known randomwalks. We also define a novel performance metric called Proximity Cover Time which, along with other metrics such us visit overlap statistics and proximity variation, we use to evaluate the performance properties and features of the various walks. Finally, we present future plans on investigating a relevant combinatorial property of Random Geometric Graphs that may lead to new, faster randomwalks and metrics.