PRIN Project COGENT “COmputational and GamE-theoretic aspects of uncoordinated NeTworks” “kick-off” project meeting Roma, 17 June 2010

List of the Research Units UNIT I: University of L’Aquila UNIT II: CNR Pisa UNIT III:University of Salerno UNIT IV:Univ. Rome “Tor Vergata” UNIT V:Univ. Rome “La Sapienza”

Research Program Emerging communication networks are characterized by decentralization, autonomy, and general lack of coordination, wireless access, heterogeneity The combination of uncoordination and wireless access requires: 1)modeling and analyzing the consequences of the autonomous users behaviour on the network performance 2)accounting for specific features imposed by the dynamic nature of these networks (e.g., users mobility, wireless medium, unreliable connectivity, etc.); 3)investigating the influence of the different degrees of users social knowledge on users behaviour when analyzing items 1) and 2) above, and, consequently, on the system performance and on the induced mobility patterns and network topology;

Our objectives are: 1)to provide a rigorous algorithmic study on the effect of autonomic non-cooperative user behaviour on the performance of large-scale uncoordinated networks, and to study strategies/solutions to discourage non-cooperativeness; 2)to explore the impact of node mobility/dynamicity on such uncoordinated networks, by adopting a foundational algorithmic approach in order to provide analytical solutions that exploit node mobility to optimize network performances; 3)to consider in the proposed solutions the effects of social relationships 4)to experimentally validate the achieved results through extensive simulation.

Methodological aspects: integration of classical algorithmic investigation with techniques and concepts borrowed from –Mathematical Economics and Game Theory –Social Netwoks

Project development and schedule 1) Milestone M1 (months 1-6): –definition of realistic algorithmic and strategic models for uncoordinated networks and determination of the main related open problems; –selection of the simulation tools to be used in the project activities; –start of co-operation between members of different sites to obtain the first results. 2) Milestone M2 (months 7-12): –dissemination of the first results by means of publications in major related international conferences and tuning of the research directions as a function of the foreseen relevance. 3) Milestone M3 (months 13-18): –improvement of achieved results and consequent extension toward new research directions, depending also on the relevance feedback obtained by the scientific community; 4) Milestone M4 (months 19-24): –consolidation of the achieved results in more systematic integrated framework, production of surveys and final deliverables of the project.

Collaboration and integration achieved by Project meetings: –between milestones –will consist of tutorial session presentation session open discussion session workgroup session Workgroup meetings: –devoted to the continuation and consolidation of the workgroup research activities started during the project meetings Exchange visits: –visits of project participants to other units for maintaining and consolidating mutual collaborations between the units. They will include also visits to international research centers (not participating to the project)

Today’s Schedule : Opening : Rome "Tor Vergata" : Salerno : Coffee break : L'Aquila : Pisa : Lunch : Rome "La Sapienza" : Meeting of local coordinators

Unit I University of L’Aquila FLAMMINI Michele (Unit Coordinator) MELIDEO Giovanna MOSCARDELLI Luca MONACO Gianpiero PROIETTI Guido (Vice Unit Coordinator) FORLIZZI Luca BILO' Davide

Topics of interest (Michele) 1.Classical optimization Optical Networks Wireless Networks 2.Algorithmic Game Theory ADM Minimization Games Isolation Games Undirected Network Design Games Convergence to Approximate Solutions in Congestion Games Stackelberg Strategies for Network Design Games 3.Social Networks and Game Theory Graphical Games Social Context Games

Topics of interest (Guido) 1.Algorithmic Game Theory Algorithmic Mechanism Design Stackelberg (network pricing) games 2.Network Optimization Connectivity fast-recovery Network shortcutting Network robustness Network verification and monitoring Interference Minimization in Ad-hoc Networks Reoptimization

Classical Optimization

Optimization in Optical Networks Scope: in optical networks, a large portion of research concentrates with the total hardware cost. This is modeled by considering different hardware components (ADMs, OADMs, regenerators) and aiming at minimizing their (combined) cost. Past works: minimization of the number of wavelengths used in an optical network. Recent results: 1.M. Flammini, M. Shalom, S. Zaks "On minimizing the number of ADMs - Tight bounds for an algorithm without preprocessing". J. Parallel Distrib. Comput. (2007), 67(4) 2.M. Flammini, L. Moscardelli, M. Shalom, S. Zaks "Approximating the Traffic Grooming Problem". Journal of Discrete Algorithms (2008), 6(3). 3.M. Flammini, G. Monaco, L. Moscardelli, M. Shalom, S. Zaks "Approximating the Tra±c Grooming Problem in Tree and Star Networks". Journal of Parallel and Distributed Computing (2008), 68(7). 4.M. Flammini, G. Monaco, L. Moscardelli, M. Shalom, S. Zaks "Approximating the Traffic Grooming Problem with respect to ADMs and OADMs". Euro-Par 2008, LNCS M. Flammini, A. Marchetti Spaccamela, G. Monaco, L. Moscardelli, S. Zaks. "On the complexity of the regenerator placement problem in optical networks". SPAA M. Flammini, M. Shalom, S. Zaks "On minimizing the number of ADMs in a general topology optical network". Discrete Applied Mathematics (2009), 157(12) 7.M. Flammini, G. Monaco, L. Moscardelli, H. Shachnai, M. Shalom, T. Tamirk, S. Zaks "Minimizing Total Busy Time in Parallel Scheduling with Application to Optical Networks“, online first on Theoretical Computer Science (2010). Open COGENT problems: Extending the obtained results to more general network topologies, tightening the results.

Optimization in Wireless Networks Scope: We consider the Minimum Energy Broadcast Routing problem in ad hoc wireless networks. The goal was that of improving the estimation of the approximation bound of the Minimum Spanning Tree (MST) heuristic and currently of designing approximation algorithms outperforming such a heuristic. In recent papers we have presented an algorithm with exponentially better approximation factor than the MST heuristic. Past works: Approximation algorithms based on the MST heuristic. Recent results: 1.M. Flammini, R. Klasing, A. Navarra, S. Perennes "Tightening the upper bound for the minimum energy broadcasting". Wireless Networks (2008), 14(5) 2.I. Caragiannis, M. Flammini, L. Moscardelli "An exponential improvement on the MST heuristic for the Minimum Energy Broadcasting problem". ICALP 2007, LNCS Open COGENT problems: tightening the current gap between the lower and upper bound for the case of Euclidean instances.

Algorithmic Game Theory

ADM Minimization Game Scope: in optical networks, a large portion of research concentrates with the total hardware cost. This is modelled by considering the basic electronic switching units of the electronic add-drop multiplexer (ADM) and focusing on the total number of these hardware components. In a distributed and decentralized environment characterizing an optical communication network, besides the classical design of centralized algorithms optimizing the resources utilization, the analysis of the uncooperative interaction between the network users and the design of distributed algorithms call for more research effort. Past works: Considered solutions from centralized point of view. Recent result: M. Flammini, G. Monaco, L. Moscardelli, M. Shalom and Z. Zaks: Selfishness, Collusion and Power of Local Search for the ADMs Minimization problem, Computer Networks, 52(9):1721–1731 (2008). A preliminary version appeared in the 3rd International Workshop On Internet And Network Economics (WINE) Open COGENT problems: Considering new cost sharing methods; extending to grooming.

Isolation Games Scope: Isolation games is a class of competitive location games in which the utility of a player is defined as a function of her distances from the other ones. For example, one can define the utility of a player as being equal to the distance from the nearest one or to the sum of the distances from all the other players, or to the distance from the l-th nearest player and so on and so forth. Past works: Studied convergence and/or existence of Nash equilibria. Recent result: V. Bilò, M. Flammini, G. Monaco and L. Moscardelli: On the performances of Nash Equilibria in Isolation Games, Journal of Combinatorial Optimization (2010), to appear. A preliminary appeared in the 15th International Computing and Combinatorics Conference (COCOON) Open COGENT problems: considering some simple spaces; different distance definitions; approximate Nash Equilibria, complexity and performances of not yet analyzed cases.

Undirected Network Design Games Scope: Network design is among the most well-studied problems in the combinatorial optimization literature. We are given a graph consisting of a set of nodes and edges among them representing potential links. Each edge has an associated cost which corresponds to the cost for establishing the corresponding link. We are also given connectivity requirements as pairs of source-destination nodes. The objective is to compute a subgraph of the original graph of minimum total cost that satisfies the connectivity requirements. In a game-theoretic variant instead of considering the connectivity requirements as a global goal, we assume that each connectivity requirement is desirable by a different selfish player. Past works: convergence to Nash Equilibria, (tight) price of Anarchy, (non- matching) Upper and Lower bound on the price of stability. Recent result: V. Bilò, I. Caragiannis, A. Fanelli and G. Monaco: Improved lower bounds on the price of stability of undirected network design games. Submitted for pubblication.. Open COGENT problems: Closing the gap between upper and lower bound on the price of stability.

Convergence to Approximate Solutions in Congestion Games Scope: Congestion games are a well established and largely studied approach to model resource sharing among selfish players. We aim at studying the number of players selfish moves needed to reach a solution having a social value not far from the social optimum. Past works: complexity results for computing Nash Equilibria, bounds on the Price of Anarchy for congestion games. Recent results: 1.V. Bilò, A. Fanelli, M. Flammini, G. Melideo, L. Moscardelli "Designing Fast Converging Cost Sharing Methods for Multicast Transmissions". Theory of Computing Systems (2010), 47(2). 2.A. Fanelli, M. Flammini, L. Moscardelli "On the Convergence of Multicast Games in Directed Networks". Algorithmica (2010), 57(2). 3.A. Fanelli, M. Flammini, L. Moscardelli "The speed of Convergence in Congestion Games under Best Response Dynamics“ ICALP 2008, LNCS Full version accepted to ACM Transaction on Algorithms (2010). 4.V. Bilò, A. Fanelli, M. Flammini, L. Moscardelli "Performances of One-Round Walks in Linear Congestion Games“, SAGT 2009, LNCS A. Fanelli, L. Moscardelli "On Best Response Dynamics in Weighted Congestion Games with Polynomial Delays“ WINE 2009, LNCS Open COGENT problems: Extending the results to more general (unrestricted) dynamics; considering the notion of approximate Nash Equilibria.

Stackelberg Strategies for Network Design Games Scope: In a Network Design game we are given a network and, for each player, a source and a destination node. Each player chooses a path connecting his source and destination node and the cost of each edge e is shared equally by the set of all players whose selected paths contain e. In the Stackelberg model, a central authority exploits a small fraction of coordinated players for improving the quality of the Nash equilibrium reached by the remaining selfish players, by assigning the coordinate players appropriately selected strategies. The goal is to apply the Stackelberg model to Network design Games, in order to reduce its high Price of Anarchy (equal to the number of players). Past works: (tight) price of Anarchy for Network Design Games, Stackelberg Strategies for other class of games such as Linear Congestion Games. Recent results: A. Fanelli, M. Flammini, L. Moscardelli: Stackelberg strategies for network design games. Submitted for pubblication. Open COGENT problems: Designing efficient Stackelberg strategies for other social functions (such as the MAX social function taking into account the maximum players cost)

Social Network and Game Theory

Social Networks and Graphical Games Scope: social network algorithmic issues are studied both from a classical point of view (by studying the Small World model introduced by Kleinberg) and from a non-cooperative one, by introducing a new framework for game theory in which the limited knowledge between players is modeled by means of a social graph in which nodes are associated to players an there is an edge between two nodes if the corresponding players know each other. Such a framework has been applied to congestion games. Past works: Small World model, bounds on the price of anarchy in congestion games, Bayesian games and games with incomplete information. Recent results: 1.M. Flammini, L. Moscardelli, A. Navarra, S. Perennes "Asymptotically Optimal Solutions for Small World Graphs". Theory of Computing Systems (2008), 42(4). 2.V. Bilò, A. Fanelli, M. Flammini, L. Moscardelli “Graphical Congestion Games“, online first on Algorithmica (2010) 3.V. Bilò, A. Fanelli, M. Flammini, L. Moscardelli "When Ignorance helps: Graphical Multicast Cost Sharing Games". Theoretical Computer Science (2010), 411(3). Open COGENT problems: Closing the gap between upper and lower bound on the price of stability.

Social Context Games Scope: in social context games a standard game is associated with a graph expresses social relationships among players. Players, starting from the immediate costs they would pay in the standard game, pay an aggregated cost given by a function of his cost and the cost of his social neighbours. The goal is characterizing the existence of equilibria for the different aggregating functions and the performance in terms of Pirce of Anarchy with respect to various social objectives. Such a framework has been applied to congestion and cost sharing games. Past works: Existence of equilibria in resource selection games. Recent results: 1.V. Bilò, A. Celi, M. Flammini, V. Gallotti "Social Context Congestion Games". Manuscript Open COGENT problems: Closing the gap between upper and lower bound on the price of anarchy, investigating the price of stability, extending to other games and and aggregating and/or social functions.

Algorithmic Game Theory

Algorithmic Mechanism Design Scope: For a given network optimization problem in which part of the input is privately held by selfish agents, convince them to cooperate with the system by honestly revealing their input types. This should be done by designing an algorithmically efficient truthful (w.r.t. to some equilibrium concept) mechanism. Past work: studied for MST, Shortest path, Single-source shortest paths tree, Minimum Diameter Spanning Tree. Recent results: 1.D. Bilò, L. Forlizzi, L. Gualà, and G. Proietti: Approximate Mechanisms for the Metric TSP and other Graph Traversal Problems, Internet Mathematics, 5(4):411–435 (2010). 2.D. Bilò, L. Gualà, and G. Proietti: Dynamic Mechanism Design, Theoretical Computer Science, 410(17): (2009). 3.P. Penna, G. Proietti, and P. Widmayer: Strongly Polynomial-Time Truthful Mechanisms in One Shot, Theoretical Computer Science, 410(17): (2009). 4.L. Gualà and G. Proietti: Exact and Approximate Truthful Mechanisms for the Shortest-Paths Tree Problem, Algorithmica, 49(3): (2007). Open COGENT problems: Generalized (multiple-item) second-price auction.

Stackelberg (network pricing) games Scope: Games with perfect information in which a leader chooses an action from a set A 1, and one or more follower, informed of the leader’s choice, chooses an action from a set A 2. Solutions of Stackelberg game correspond to solutions of a bilevel optimization problem. Past work: Studied for MST, Shortest path, Single-source shortest paths tree. Recent results: 1.D. Bilò, L. Gualà, and G. Proietti: Hardness of a 2-player asymmetric Stackelberg network pricing game, Electronic Colloquium on Computational Complexity (ECCC), (112), D. Bilò, L. Gualà, G. Proietti, and P. Widmayer: Computational Aspects of a 2- player Stackelberg Shortest Paths Tree Game, 4th International Workshop on Internet & Network Economics (WINE'08), December 17-20, 2008, Shanghai, China, Vol of LNCS, pages , Springer, Open COGENT problems: Placement games, Pricing games with fair allocation

Network Optimization

Network connectivity fast- recovery Scope: If a network component fails only temporarily, and is supposed to be back to be operational soon, then instead of recomputing a solution from scratch it may be more productive to compute an "emergency network" which makes use of all the unaffected components, plus a set of temporary replacement components; clearly the problem here is to compute efficiently these components. Past work: studied for MST, Shortest path, Single-source shortest paths tree, Minimum Diameter Spanning Tree. Recent results: 1.D. Bilò, L. Gualà, and G. Proietti: Finding Best Swap Edges Minimizing the Routing Cost of a Spanning Tree, 35th Mathematical Foundations of Computer Science (MFCS’10), August 23-27, 2010, Brno, Czech Republic. 2.A. Di Salvo and G. Proietti: Swapping a Failing Edge of a Shortest Paths Tree by Minimizing the Average Stretch Factor, Theoretical Computer Science, 383(1):23-33 (2007). Open COGENT problems: Extending the approach to other interesting network topologies.

Network shortcutting Scope: Given a (either weighted or unweighted) graph, augment it with a (approximately) minimum total-length set of edges so as to reduce a prescribed network feature (e.g., diameter, set of shortest paths, etc.). Past work: studied for diameter and shortest-paths. Recent results: 1.D. Bilò, L. Gualà, and G. Proietti: Improved Approximability and Non- approximability Results for Graph Diameter Decreasing Problems, 35th Mathematical Foundations of Computer Science (MFCS’10), August 23-27, 2010, Brno, Czech Republic. Open COGENT problems: Extension to other interesting features, like the max-radius of a given clustering.

Network robustness Scope: in this class of graph problems, each edge weight is uncertain, i.e., it is not a fixed value; thus, classic problems on graphs like computing a shortest path between two nodes, must be rephrased as computing a *robust* short path between two nodes, namely a path which is quite good for any of the possible input values of the edge weights. Past work: studied for MST and Shortest path. Recent results: 1.D. Bilò, M. Gatto, L. Gualà, G. Proietti, and P. Widmayer: Stability of Networks in Stretchable Graphs, 16th Colloquium on Structural Information and Communication Complexity (SIROCCO'09), May 25-27, 2009, Piran, Slovenia, Vol of LNCS, pages , Springer, Open COGENT problems: Extension to other interesting network topologies, like the Minimum Diameter Spanning Tree.

Network verification and monitoring Scope: in this class of problems, an input graph is given, and one has to verify the input (or at least some of its features) by minimizing the number of queried nodes, where a query at a node returns a certain set of information about the graph (e.g., the distance of every other node to the queried one, the routing tables, etc.) Past work: studied for some query models and some graph topologies. Recent results: 1.D. Bilò, G. Drovandi, L. Gualà, and G. Proietti: Verifying Basic Graph Topologies through Routing Tables Queries, work in progress. 2.D. Bilò, T. Erlebach, M. Mihalák, and P. Widmayer: Discovery of Network Properties with All-shortest-paths Queries, Theoretical Computer Science, 411(14-15): (2010). Open COGENT problems: Extension to other interesting graph topologies, like regular graphs.

Interference Minimization in Ad-hoc Networks Scope: in this class of problems, we are given a set of nodes (wireless devices) that need to implement a given communication protocol. The goal is to implement the protocol by minimizing a given interference measure. Past work: studied for broadcasting and gossiping and for some interference measures. Recent results: 1.D. Bilò and G. Proietti: On the complexity of minimizing interference in ad-hoc and sensor networks. Theoretical Computur Science 402(1): (2008). Open COGENT problems: Extension to other interesting protocols/interference measures.

Reoptimization Scope: in this class of problems, we suppose to have at hand an optimal solution of a computationally hard network design problem, and as a consequence of a network component perturbation, we try to recompute an optimal solution by exploiting the knowledge of the former optimal solution; Past work: TSP, Vertex Cover, Steiner Tree. Recent results: 1.H.-J. Böckenhauer, L. Forlizzi, J. Hromkovic, J. Kneis, J. Kupke, G. Proietti, and P. Widmayer: On the Approximability of TSP on Local Modifications of Optimally Solved Instances, Algorithmic Operations Research, 2(2):83-93 (2007). 2.D. Bilò, P. Widmayer and A. Zych: Reoptimization of Weighted Graph and Covering Problems, 6th Int. Workshop on Approximation and Online Algorithms (WAOA’08), ), Vol of LNCS, pages 201–213. Springer, D. Bilò, H.-J. Böckenhauer, D. Komm, R. Kralovic, T. Momke, S. Seibert, and A. Zych: Reoptimization of the Shortest Common Superstring Problem, 20th Combinatorial Pattern Matching (CPM'09), Vol of LNCS, pages 78–91. Springer, Open COGENT problems: Extending the approach to other network problems of interest.