Ameya Hate

Approximability of the Firefighter Problem: Computing Cuts over Time

We provide approximation algorithms for several variants of the Firefighter problem on general graphs. The Firefighter problem models the case where a diffusive process such as an infection (or an idea, a computer virus, a fire) is spreading through a network, and our goal is to contain this infection by using targeted vaccinations. Specifically, we are allowed to vaccinate at most a fixed number (called the budget) of nodes per time step, with the goal of minimizing the effect of the infection. The difficulty of this problem comes from its temporal component, since we must choose nodes to vaccinate at every time step while the infection is spreading through the network, leading to notions of “cuts over time”.We consider two versions of the Firefighter problem: a “non-spreading” model, where vaccinating a node means only that this node cannot be infected; and a “spreading” model where the vaccination itself is an infectious process, such as in the case where the infection is a harmful idea, and the vaccine to it is another infectious beneficial idea. We look at two measures: the MaxSave measure in which we want to maximize the number of nodes which are not infected given a fixed budget, and the MinBudget measure, in which we are given a set of nodes which we have to save and the goal is to minimize the budget. We study the approximability of these problems in both models.

Seeding influential nodes in non-submodular models of information diffusion

We consider the model of information diffusion in social networks from Hui et al. (Agentbased simulation of the diffusion of warnings, 2010) which incorporates trust (weighted links) between actors, and allows actors to actively participate in the spreading process, specifically through the ability to query friends for additional information. This model captures how social agents transmit and act upon information more realistically as compared to the simpler threshold and cascade models. However, it is more difficult to analyze, in particular with respect to seeding strategies. We present efficient, scalable algorithms for determining good seed sets—initial nodes to inject with the information. Our general approach is to reduce our model to a class of simpler models for which provably good sets can be constructed. By tuning this class of simpler models, we obtain a good seed set for the original more complex model. We call this the projected greedy approach because a model is ‘projected’ onto a class of simpler models where the greedy seed set selection is near-optimal. We demonstrate the effectiveness of our seeding strategy on synthetic graphs as well as a realistic San Diego evacuation network constructed during the 2007 fires, and the DBLP network of collaborations.

Strategic pricing in next-hop routing with elastic demands

We consider a model of next-hop routing by self-interested agents. In this model, nodes in a graph (representing ISPs, Autonomous Systems, etc.) make pricing decisions of how much to charge for forwarding traffic from each of their upstream neighbors, and routing decisions of which downstream neighbors to forward traffic to (i.e., choosing the next hop). Traffic originates at a subset of these nodes that derive a utility when the traffic is routed to its destination node; the traffic demand is elastic and the utility derived from it can be different for different source nodes. Our next-hop routing and pricing model is in sharp contrast with the more common source routing and pricing models, in which the source of traffic determines the entire route from source to destination. For our model, we begin by showing sufficient conditions for prices to result in a Nash equilibrium, and in fact give an efficient algorithm to compute a Nash equilibrium which is as good as the centralized optimum, thus proving that the price of stability is 1. When only a single source node exists, then the price of anarchy is 1 as well, as long as some minor assumptions on player behavior is made. The above results hold for arbitrary convex pricing functions, but with the assumption that the utilities derived from getting traffic to its destination are linear. When utilities can be non-linear functions, we show that Nash equilibrium may not exist, even with simple discrete pricing models.

Strategic Multiway Cut and Multicut Games

We consider cut games where players want to cut themselves off from different parts of a network. These games arise when players want to secure themselves from areas of potential infection. For the game-theoretic version of Multiway Cut, we prove that the price of stability is 1, i.e., there exists a Nash equilibrium as good as the centralized optimum. For the game-theoretic version of Multicut, we show that there exists a 2-approximate equilibrium as good as the centralized optimum. We also give poly-time algorithms for finding exact and approximate equilibria in these games.

Strategic multiway cut and multicut games

We consider cut games where players want to cut themselves off from different parts of a network. These games arise when players want to secure themselves from areas of potential infection. For the game-theoretic version of Multiway Cut, we prove that the price of stability is 1, i.e., there exists a Nash equilibrium as good as the centralized optimum. For the game-theoretic version of Multicut, we show that there exists a 2-approximate equilibrium as good as the centralized optimum. We also give poly-time algorithms for finding exact and approximate equilibria in these games.

Partition equilibrium always exists in resource selection games

We consider the existence of Partition Equilibrium in Resource Selection Games. Super-strong equilibrium, where no subset of players has an incentive to change their strategies collectively, does not always exist in such games. We show, however, that partition equilibrium (introduced in [4] to model coalitions arising in a social context) always exists in general resource selection games, as well as how to compute it efficiently. In a partition equilibrium, the set of players has a fixed partition into coalitions, and the only deviations considered are by coalitions that are sets in this partition. Our algorithm to compute a partition equilibrium in any resource selection game (i.e., load balancing game) settles the open question from [4] about existence of partition equilibrium in general resource selection games. Moreover, we show how to always find a partition equilibrium which is also a Nash equilibrium. This implies that in resource selection games, we do not need to sacrifice the stability of individual players when forming solutions stable against coalitional deviations. In addition, while super-strong equilibrium may not exist in resource selection games, we show that its existence can be decided efficiently, and how to find one if it exists.