arXiv subjects

Gideon Blocq

Publications and source records attributed to Gideon Blocq.

3 recordsLinked to original sources

arXiv2018

Offline and Online Models of Budget Allocation for Maximizing Influence Spread

The research of influence propagation in social networks via word-of-mouth processes has been given considerable attention in recent years. Arguably, the most fundamental problem in this domain is influence maximization, where the goal is to identify a seed set of individuals that can trigger a large cascade of influence in the network. While there has been significant progress regarding this problem and its variants, one basic shortcoming of the models is that they lack the flexibility in the way the budget is allocated to individuals. Indeed, budget allocation is a critical issue in advertising and viral marketing. Taking the other point of view, known models allowing flexible budget allocation do not take into account the influence spread in the network. We introduce a generalized model that captures both budgets and influence propagation simultaneously. For the offline setting, we identify a large family of budget-based propagation functions that admit tight approximation guarantee. This family extends most of the previously studied influence models, including the well-known Triggering model. We establish that any function in this family implies an instance of a monotone submodular function maximization over the integer lattice subject to a knapsack constraint. This problem is known to admit an optimal (1-1/e)-approximation. We also study the price of anarchy of the multi-player game that extends the model and establish tight results. For the online setting, in which an unknown subset of agents arrive in a random order and the algorithm needs to make an irrevocable budget allocation in each step, we develop a 1/(15e)-competitive algorithm. This setting extends the secretary problem, and its variant, the submodular knapsack secretary problem. Notably, our algorithm improves over the best known approximation for the latter problem, even though it applies to a more general setting.

cs.DS↗

arXiv2016

Coalitions in Routing Games: A Worst-Case Perspective

We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the coalition can guarantee itself, under any (including worst) conditions. We then investigate fundamental solution concepts of the considered cooperative game, namely the core and a variant of the min-max fair nucleolus. We consider two types of routing games based on the agents' Performance Objectives, namely bottleneck routing games and additive routing games. For bottleneck games we establish that the core includes all system-optimal flow profiles and that the nucleolus is system-optimal or disadvantageous for the smallest agent in the system. Moreover, we describe an interesting set of scenarios for which the nucleolus is always system-optimal. For additive games, we focus on the fundamental load balancing game of routing over parallel links. We establish that, in contrary to bottleneck games, not all system-optimal flow profiles lie in the core. However, we describe a specific system-optimal flow profile that does lie in the core and, under assumptions of symmetry, is equal to the nucleolus.

cs.NI↗

arXiv2016

How Good is Bargained Routing?

In the context of networking, research has focused on non-cooperative games, where the selfish agents cannot reach a binding agreement on the way they would share the infrastructure. Many approaches have been proposed for mitigating the typically inefficient operating points. However, in a growing number of networking scenarios selfish agents are able to communicate and reach an agreement. Hence, the degradation of performance should be considered at an operating point of a cooperative game. Accordingly, our goal is to lay foundations for the application of cooperative game theory to fundamental problems in networking. We explain our choice of the Nash Bargaining Scheme (NBS) as the solution concept, and introduce the Price of Selfishness (PoS), which considers the degradation of performance at the worst NBS. We focus on the fundamental load balancing game of routing over parallel links. First, we consider agents with identical performance objectives. We show that, while the PoA here can be large, through bargaining, all agents, and the system, strictly improve their performance. Interestingly, in a two-agent system or when all agents have identical demands, we establish that they reach social optimality. We then consider agents with different performance objectives and demonstrate that the PoS and PoA can be unbounded, yet we explain why both measures are unsuitable. Accordingly, we introduce the Price of Heterogeneity (PoH), as an extension of the PoA. We establish an upper-bound on the PoH and indicate its further motivation for bargaining. Finally, we discuss network design guidelines that follow from our findings

cs.NI↗