Flow Games

In the traditional maximal-flow problem, the goal is to transfer maximum flow in a network by directing, in each vertex in the network, incoming flow into outgoing edges. While the problem has been extensively used in order to optimize the performance of networks in numerous application areas, it corresponds to a setting in which the authority has control on all vertices of the network. Today\u27s computing environment involves parties that should be considered adversarial. We introduce and study {em flow games}, which capture settings in which the authority can control only part of the vertices. In these games, the vertices are partitioned between two players: the authority and the environment. While the authority aims at maximizing the flow, the environment need not cooperate. We argue that flow games capture many modern settings, such as partially-controlled pipe or road systems or hybrid software-defined communication networks. We show that the problem of finding the maximal flow as well as an optimal strategy for the authority in an acyclic flow game is $Sigma_2^P$-complete, and is already $Sigma_2^P$-hard to approximate. We study variants of the game: a restriction to strategies that ensure no loss of flow, an extension to strategies that allow non-integral flows, which we prove to be stronger, and a dynamic setting in which a strategy for a vertex is chosen only once flow reaches the vertex. We discuss additional variants and their applications, and point to several interesting open problems

The Unfortunate-Flow Problem

In the traditional maximum-flow problem, the goal is to transfer maximum flow in a network by directing, in each vertex in the network, incoming flow into outgoing edges. The problem is one of the most fundamental problems in TCS, with application in numerous domains. The fact a maximal-flow algorithm directs the flow in all the vertices of the network corresponds to a setting in which the authority has control in all vertices. Many applications in which the maximal-flow problem is applied involve an adversarial setting, where the authority does not have such a control. We introduce and study the unfortunate flow problem, which studies the flow that is guaranteed to reach the target when the edges that leave the source are saturated, yet the most unfortunate decisions are taken in the vertices. When the incoming flow to a vertex is greater than the outgoing capacity, flow is lost. The problem models evacuation scenarios where traffic is stuck due to jams in junctions and communication networks where packets are dropped in overloaded routers. We study the theoretical properties of unfortunate flows, show that the unfortunate-flow problem is co-NP-complete and point to polynomial fragments. We introduce and study interesting variants of the problem: integral unfortunate flow, where the flow along edges must be integral, controlled unfortunate flow, where the edges from the source need not be saturated and may be controlled, and no-loss controlled unfortunate flow, where the controlled flow must not be lost

Atomic dynamic flow games : adaptive versus nonadaptive agents

We propose a game model for selfish routing of atomic agents, who compete for use of a network to travel from their origins to a common destination as fast as possible. We follow a frequently used rule that the latency an agent experiences on each edge is a constant transit time plus a variable waiting time in a queue. A key feature that differentiates our model from related ones is an edge-based tie-breaking rule for prioritizing agents in queueing when they reach an edge at the same time. We study both nonadaptive agents (each choosing a one-off origin-destination path simultaneously at the very beginning) and adaptive ones (each making an online decision at every nonterminal vertex they reach as to which next edge to take). On the one hand, we constructively prove that a (pure) Nash equilibrium (NE) always exists for nonadaptive agents, and show that every NE is weakly Pareto optimal and globally first-in-first-out. We present efficient algorithms for finding an NE and best responses of nonadaptive agents. On the other hand, we are among the first to consider adaptive atomic agents, for which we show that a subgame perfect equilibrium (SPE) always exists, and that each NE outcome for nonadaptive agents is an SPE outcome for adaptive agents, but not vice versa

Optimal coalition structure generation on large-scale renewable energy smart grids

Most renewable energy sources are dependent on unpredictable weather conditions, which have considerable variation over space and time. The intermittent nature of this production means that any renewable energy prosumer may sometimes produce an amount of energy in excess of its local consumption needs and sometimes in deficiency. This thesis is concerned with developing methods that can improve the effectiveness and widespread adoption of renewable energy usage. In order for renewable energy to be more economically viable, there needs to be a scheme for sharing energy among the prosumers so that those with excess energy can give their excess amounts to those in energy deficiency. That is the task addressed in this thesis. The way to deal with this problem is to setup an optimal arrangement of local coalitions of renewable energy prosumers such that energy is shared within the coalitions in an optimally efficient manner. As is formally explained early on in this work, finding such an optimal coalition arrangement is an example of a Coalition Structure Generation (CSG) problem. The most straightforward way to find an optimal solution for a given pool of prosumer agents in these circumstances is to examine every possible coalition partition (coalition structure) and evaluate its comparative utility. This is known as ``exhaustive search'' (ES) and can be computationally expensive. As has been shown earlier, the number of such evaluations in ES even for a pool of twenty agents can be in the tens of trillions. The problem for us in the renewable energy domain is that, because of the constantly changing weather conditions among the scattered prosumers, the CSG optimization calculation must be carried out every hour of the day. This means that the ES approach in the CSG optimization calculation for a reasonable number of prosumer agents is computationally intractable. So a more computationally feasible stochastic optimization method must be used, which searches through the coalition structure search space in order to find a reasonably good solution even if it is not the global optimum. To this end, a number of stochastic optimization search methods have been investigated in this thesis, including some of our own novel extensions to existing approaches. These search methods have been examined with respect to two different connection arrangements with respect to the outside world – (1) when the local prosumer networks have a connection to a public utility power grid and can therefore buy needed energy (at a high price) from the grid and sell excess energy (at a low price) to the grid and (2) when the local prosumer networks are isolated from any public utility, which is referred to as ``island mode''. The overall goal of these investigations has been to find an optimization approach that arrives at a near-optimal (near the global optimum of the given search space) that is computationally efficient (i.e. it does not require a vast amount of computer memory or running time). Based on these empirical examinations, which have employed realistic parameters drawn from existing consumption and renewable energy data sets, the following conclusions concerning renewable energy can be drawn from this study: • It is feasible to employ ordinary computer resources to obtain on an hourly basis near-optimal energy-sharing coalition structures that will lead to the more effective and economical use of renewable energy. • This energy-sharing approach will contribute to more rapid adoption and proliferation of existing renewable energy equipment and infrastructure. The principal contributions towards these end that this thesis work has made are as follows: • A modelling framework has been set up that can be used for extensive empirical determinations of near-optimal energy-sharing coalition structures. • A detailed empirical study has been carried out that has examined the relative capabilities in this context of various optimal coalition structure search methods, including genetic algorithms (GA), dynamic programming (DP), particle swarm optimization (PSO), population-based incremental learning (PBIL), and several variants to PBIL. • The novel extensions to basic PBIL optimization have included Top-k Merit Weighting PBIL (PBIL-MW), Set-ID Encoding Schemes, and Hierarchical PBIL-MW