76 research outputs found

### On the Feasibility of Maintenance Algorithms in Dynamic Graphs

Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly disconnected) graph over time naturally leads to the important complexity question: is it better to calculate a new solution from scratch or to adapt the known solution on the prior graph to quickly provide a solution of guaranteed quality for the changed graph? In this paper, we demonstrate that the former is the best approach in some cases, but that there are cases where the latter is feasible. We prove that, under certain conditions, hard problems cannot even be approximated in any reasonable complexity bound --- i.e., even with a large amount of time, having a solution to a very similar graph does not help in computing a solution to the current graph. To achieve this, we formalize the idea as a maintenance algorithm. Using r-Regular Subgraph as the primary example we show that W[1]-hardness for the parameterized approximation problem implies the non-existence of a maintenance algorithm for the given approximation ratio. Conversely we show that Vertex Cover, which is fixed-parameter tractable, has a 2-approximate maintenance algorithm. The implications of NP-hardness and NPO-hardness are also explored

### On the Treewidth of Dynamic Graphs

Dynamic graph theory is a novel, growing area that deals with graphs that
change over time and is of great utility in modelling modern wireless, mobile
and dynamic environments. As a graph evolves, possibly arbitrarily, it is
challenging to identify the graph properties that can be preserved over time
and understand their respective computability.
In this paper we are concerned with the treewidth of dynamic graphs. We focus
on metatheorems, which allow the generation of a series of results based on
general properties of classes of structures. In graph theory two major
metatheorems on treewidth provide complexity classifications by employing
structural graph measures and finite model theory. Courcelle's Theorem gives a
general tractability result for problems expressible in monadic second order
logic on graphs of bounded treewidth, and Frick & Grohe demonstrate a similar
result for first order logic and graphs of bounded local treewidth.
We extend these theorems by showing that dynamic graphs of bounded (local)
treewidth where the length of time over which the graph evolves and is observed
is finite and bounded can be modelled in such a way that the (local) treewidth
of the underlying graph is maintained. We show the application of these results
to problems in dynamic graph theory and dynamic extensions to static problems.
In addition we demonstrate that certain widely used dynamic graph classes
naturally have bounded local treewidth

### Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some
apparently unrelated areas of dynamic systems -- delay-tolerant networks,
opportunistic-mobility networks, social networks -- obtaining closely related
insights. Indeed, the concepts discovered in these investigations can be viewed
as parts of the same conceptual universe; and the formal models proposed so far
to express some specific concepts are components of a larger formal description
of this universe. The main contribution of this paper is to integrate the vast
collection of concepts, formalisms, and results found in the literature into a
unified framework, which we call TVG (for time-varying graphs). Using this
framework, it is possible to express directly in the same formalism not only
the concepts common to all those different areas, but also those specific to
each. Based on this definitional work, employing both existing results and
original observations, we present a hierarchical classification of TVGs; each
class corresponds to a significant property examined in the distributed
computing literature. We then examine how TVGs can be used to study the
evolution of network properties, and propose different techniques, depending on
whether the indicators for these properties are a-temporal (as in the majority
of existing studies) or temporal. Finally, we briefly discuss the introduction
of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be
published in Internation Journal of Parallel, Emergent and Distributed
System

### Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned
at different nodes of a network to group within finite time at the same
location, not fixed in advanced.
The extensive existing literature on this problem shares the same fundamental
assumption: the topological structure does not change during the rendezvous or
the gathering; this is true also for those investigations that consider faulty
nodes. In other words, they only consider static graphs. In this paper we start
the investigation of gathering in dynamic graphs, that is networks where the
topology changes continuously and at unpredictable locations.
We study the feasibility of gathering mobile agents, identical and without
explicit communication capabilities, in a dynamic ring of anonymous nodes; the
class of dynamics we consider is the classic 1-interval-connectivity.
We focus on the impact that factors such as chirality (i.e., a common sense
of orientation) and cross detection (i.e., the ability to detect, when
traversing an edge, whether some agent is traversing it in the other
direction), have on the solvability of the problem. We provide a complete
characterization of the classes of initial configurations from which the
gathering problem is solvable in presence and in absence of cross detection and
of chirality. The feasibility results of the characterization are all
constructive: we provide distributed algorithms that allow the agents to
gather. In particular, the protocols for gathering with cross detection are
time optimal. We also show that cross detection is a powerful computational
element.
We prove that, without chirality, knowledge of the ring size is strictly more
powerful than knowledge of the number of agents; on the other hand, with
chirality, knowledge of n can be substituted by knowledge of k, yielding the
same classes of feasible initial configurations

### Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots

A graph environment must be explored by a collection of mobile robots. Some
of the robots, a priori unknown, may turn out to be unreliable. The graph is
weighted and each node is assigned a deadline. The exploration is successful if
each node of the graph is visited before its deadline by a reliable robot. The
edge weight corresponds to the time needed by a robot to traverse the edge.
Given the number of robots which may crash, is it possible to design an
algorithm, which will always guarantee the exploration, independently of the
choice of the subset of unreliable robots by the adversary? We find the optimal
time, during which the graph may be explored. Our approach permits to find the
maximal number of robots, which may turn out to be unreliable, and the graph is
still guaranteed to be explored.
We concentrate on line graphs and rings, for which we give positive results.
We start with the case of the collections involving only reliable robots. We
give algorithms finding optimal times needed for exploration when the robots
are assigned to fixed initial positions as well as when such starting positions
may be determined by the algorithm. We extend our consideration to the case
when some number of robots may be unreliable. Our most surprising result is
that solving the line exploration problem with robots at given positions, which
may involve crash-faulty ones, is NP-hard. The same problem has polynomial
solutions for a ring and for the case when the initial robots' positions on the
line are arbitrary.
The exploration problem is shown to be NP-hard for star graphs, even when the
team consists of only two reliable robots

### Computational Controversy

Climate change, vaccination, abortion, Trump: Many topics are surrounded by
fierce controversies. The nature of such heated debates and their elements have
been studied extensively in the social science literature. More recently,
various computational approaches to controversy analysis have appeared, using
new data sources such as Wikipedia, which help us now better understand these
phenomena. However, compared to what social sciences have discovered about such
debates, the existing computational approaches mostly focus on just a few of
the many important aspects around the concept of controversies. In order to
link the two strands, we provide and evaluate here a controversy model that is
both, rooted in the findings of the social science literature and at the same
time strongly linked to computational methods. We show how this model can lead
to computational controversy analytics that have full coverage over all the
crucial aspects that make up a controversy.Comment: In Proceedings of the 9th International Conference on Social
Informatics (SocInfo) 201

### Temporal Network Optimization Subject to Connectivity Constraints

In this work we consider temporal networks, i.e. networks defined by a labeling Î» 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 Î» 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 Mengerâ€™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

### Farsighted Risk Mitigation of Lateral Movement Using Dynamic Cognitive Honeypots

Lateral movement of advanced persistent threats has posed a severe security
challenge. Due to the stealthy and persistent nature of the lateral movement,
defenders need to consider time and spatial locations holistically to discover
latent attack paths across a large time-scale and achieve long-term security
for the target assets. In this work, we propose a time-expanded random network
to model the stochastic service links in the user-host enterprise network and
the adversarial lateral movement. We design cognitive honeypots at idle
production nodes and disguise honey links as service links to detect and deter
the adversarial lateral movement. The location of the honeypot changes randomly
at different times and increases the honeypots' stealthiness. Since the
defender does not know whether, when, and where the initial intrusion and the
lateral movement occur, the honeypot policy aims to reduce the target assets'
Long-Term Vulnerability (LTV) for proactive and persistent protection. We
further characterize three tradeoffs, i.e., the probability of interference,
the stealthiness level, and the roaming cost. To counter the curse of multiple
attack paths, we propose an iterative algorithm and approximate the LTV with
the union bound for computationally efficient deployment of cognitive
honeypots. The results of the vulnerability analysis illustrate the bounds,
trends, and a residue of LTV when the adversarial lateral movement has infinite
duration. Besides honeypot policies, we obtain a critical threshold of
compromisability to guide the design and modification of the current system
parameters for a higher level of long-term security. We show that the target
node can achieve zero vulnerability under infinite stages of lateral movement
if the probability of movement deterrence is not less than the threshold

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