Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems

In many wireless networks, there is no fixed physical backbone nor centralized network management. The nodes of such a network have to self-organize in order to maintain a virtual backbone used to route messages. Moreover, any node of the network can be a priori at the origin of a malicious attack. Thus, in one hand the backbone must be fault-tolerant and in other hand it can be useful to monitor all network communications to identify an attack as soon as possible. We are interested in the minimum \emph{Connected Vertex Cover} problem, a generalization of the classical minimum Vertex Cover problem, which allows to obtain a connected backbone. Recently, Delbot et al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant approximation ratio of $2$ for this problem. In this paper, we propose a distributed and self-stabilizing version of their algorithm with the same approximation guarantee. To the best knowledge of the authors, it is the first distributed and fault-tolerant algorithm for this problem. The approach followed to solve the considered problem is based on the construction of a connected minimal clique partition. Therefore, we also design the first distributed self-stabilizing algorithm for this problem, which is of independent interest

A Comprehensive Survey of In-Band Control in SDN: Challenges and Opportunities

Software-Defined Networking (SDN) is a thriving networking architecture that has gained popularity in recent years, particularly as an enabling technology to foster paradigms like edge computing. SDN separates the control and data planes, which are later on synchronised via a control protocol such as OpenFlow. In-band control is a type of SDN control plane deployment in which the control and data planes share the same physical network. It poses several challenges, such as security vulnerabilities, network congestion, or data loss. Nevertheless, despite these challenges, in-band control also presents significant opportunities, including improved network flexibility and programmability, reduced costs, and increased reliability. Benefiting from the previous advantages, diverse in-band control designs exist in the literature, with the objective of improving the operation of SDN networks. This paper surveys the different approaches that have been proposed so far towards the advance in in-band SDN control, based on four main categories: automatic routing, fast failure recovery, network bootstrapping, and distributed control. Across these categories, detailed summary tables and comparisons are presented, followed by a discussion on current trends a challenges in the field. Our conclusion is that the use of in-band control in SDN networks is expected to drive innovation and growth in the networking industry, but efforts for holistic and full-fledged proposals are still needed

Distributed Detection of Cycles

Distributed property testing in networks has been introduced by Brakerski and Patt-Shamir (2011), with the objective of detecting the presence of large dense sub-networks in a distributed manner. Recently, Censor-Hillel et al. (2016) have shown how to detect 3-cycles in a constant number of rounds by a distributed algorithm. In a follow up work, Fraigniaud et al. (2016) have shown how to detect 4-cycles in a constant number of rounds as well. However, the techniques in these latter works were shown not to generalize to larger cycles $C_k$ with $k\geq 5$. In this paper, we completely settle the problem of cycle detection, by establishing the following result. For every $k\geq 3$, there exists a distributed property testing algorithm for $C_k$-freeness, performing in a constant number of rounds. All these results hold in the classical CONGEST model for distributed network computing. Our algorithm is 1-sided error. Its round-complexity is $O(1/\epsilon)$ where $\epsilon\in(0,1)$ is the property testing parameter measuring the gap between legal and illegal instances

Combinatorics and geometry of finite and infinite squaregraphs

Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not incident with the outer face) have degrees larger than three. The planar dual of a finite squaregraph is determined by a triangle-free chord diagram of the unit disk, which could alternatively be viewed as a triangle-free line arrangement in the hyperbolic plane. This representation carries over to infinite plane graphs with finite vertex degrees in which the balls are finite squaregraphs. Algebraically, finite squaregraphs are median graphs for which the duals are finite circular split systems. Hence squaregraphs are at the crosspoint of two dualities, an algebraic and a geometric one, and thus lend themselves to several combinatorial interpretations and structural characterizations. With these and the 5-colorability theorem for circle graphs at hand, we prove that every squaregraph can be isometrically embedded into the Cartesian product of five trees. This embedding result can also be extended to the infinite case without reference to an embedding in the plane and without any cardinality restriction when formulated for median graphs free of cubes and further finite obstructions. Further, we exhibit a class of squaregraphs that can be embedded into the product of three trees and we characterize those squaregraphs that are embeddable into the product of just two trees. Finally, finite squaregraphs enjoy a number of algorithmic features that do not extend to arbitrary median graphs. For instance, we show that median-generating sets of finite squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure

Cheating Prevention in Peer-to-Peer-based Massively Multiuser Virtual Environments

Massively multiuser virtual environments (MMVEs) have become an increasingly popular Internet application in recent years. Until now, they are all based on client/server technology. Due to its inherent lack of scalability, realizing MMVEs based on peer-to-peer technology has received a lot of interest. From the perspective of the operator, using peer-to-peer technology raises additional challenges: the lack of trust in peers and their unreliability. The simulation of the virtual environment is governed by certain rules specified by the operator. These rules state what actions can be taken by users in the virtual environment and how the state of the environment changes based on these actions. Since MMVEs are very often competitive environments, some people will cheat and try to break the rules to get an unfair advantage over others. Using a central server performing the simulation of the virtual environment, the operator can ensure only allowed actions can be performed and the state of the environment evolves according to the rules. In a peer-to-peer setting, the operator has no control over the peers so they might not behave as implemented by the operator. Furthermore, a central server is inherently more reliable than a peer which could fail at any time so data might be lost. This thesis presents the design of a storage performing a distributed simulation of a virtual environment. It uses a deterministic event-based simulation to calculate the state of the virtual environment only based on the actions of its users. There are multiple replicated simulations using a voting mechanism to overcome the influence of malicious peers trying to tamper with the state of the environment as long as the number of malicious peers does not reach a critical threshold. Replication of data also ensures data is not lost when peers fail. The storage is based on a peer-to-peer overlay allowing peers to exchange messages to store and retrieve data. It creates a Delaunay graph structure matching the way the data in the virtual environment is distributed among the peers. A self-stabilizing algorithm keeps the structure intact as peers join and leave the network. Additional routing tables allow peers to retrieve stored replicas independently on short, disjoint paths reducing the influence of malicious peers on the retrieval of data. A redundant filling algorithm prevents malicious peers from tampering with these routing tables to get more messages routed their way

Vehicle re-routing strategies for congestion avoidance

Traffic congestion causes driver frustration and costs billions of dollars annually in lost time and fuel consumption. This dissertation introduces a cost-effective and easily deployable vehicular re-routing system that reduces the effects of traffic congestion. The system collects real-time traffic data from vehicles and road-side sensors, and computes proactive, individually tailored re-routing guidance, which is pushed to vehicles when signs of congestion are observed on their routes. Subsequently, this dissertation proposes and evaluates two classes of re-routing strategies designed to be incorporated into this system, namely, Single Shortest Path strategies and Multiple Shortest Paths Strategies. These strategies are firstly implemented in a centralized system, where a server receives traffic updates from cars, computes alternative routes, and pushes them as guidance to drivers. The extensive experimental results show that the proposed strategies are capable of reducing the travel time comparable to a state-of-the-art Dynamic Traffic Assignment (DTA) algorithm, while avoiding the issues that make DTA impractical, such as lack of scalability and robustness, and high computation time. Furthermore, the variety of proposed strategies allows the system to be tuned to different levels of trade-off between re-routing effectiveness and computational efficiency. Also, the proposed traffic guidance system is robust even if many drivers ignore the guidance, or if the system adoption rate is relatively low. The centralized system suffers from two intrinsic problems: the central server has to perform intensive computation and communication with the vehicles in real-time, which can make such solutions infeasible for large regions with many vehicles; and driver privacy is not protected since the drivers have to share their location as well as the origins and destinations of their trips with the server, which may prevent the adoption of such solutions. To address these problems, a hybrid vehicular re-routing system is presented in this dissertation. The system off-loads a large part of the re-routing computation at the vehicles, and thus, the re-routing process becomes practical in real-time. To make collaborative re-routing decisions, the vehicles exchange messages over vehicular ad hoc networks. The system is hybrid because it still uses a server to determine an accurate global view of the traffic. In addition, the user privacy is balanced with the re-routing effectiveness. The simulation results demonstrate that, compared with a centralized system, the proposed hybrid system increases the user privacy substantially, while the re-routing effectiveness is minimally impacted

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM