Jean-François Baffier

Parametric Multiroute Flow and Its Application to Robust Network with k Edge Failures

In this work, we investigate properties of the function taking the real value \(h\) to the max \(h\)-route flow value, and apply the result to solve robust network flow problems. We show that the function is piecewise hyperbolic, and modify a parametric optimization technique, the ES algorithm, to find this function. The running time of the algorithm is \(O(\lambda mn)\), when \(\lambda \) is a source-sink edge connectivity of our network, \(m\) is the number of links, and \(n\) is the number of nodes. We can use the result from that algorithm to solve two max-flow problems against \(k\) edge failures, referred to as max-MLA-robust flow and max-MLA-reliable flow. When \(h\) is optimally chosen from the function, we show that the max-\(h\)-route flow is an exact solution of both problems for graphs in a specific class. Our numerical experiments show that \(98\,\%\) of random graphs generated in the experiment are in that specific class. Given a parametric edge \(e\), we also show that the function taking the capacity of \(e\) to the max-\(h\)-route flow value is linear piecewise. Hence we can apply our modified ES algorithm to find that function in \(O(h^2mn)\).

Gap-Planar Graphs

We introduce the family of k-gap-planar graphs for \(k \ge 0\), i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most k of its crossings. This definition finds motivation in edge casing, as a \(k\)-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density, drawability of complete graphs, complexity of the recognition problem, and relationships with other families of beyond-planar graphs.

Hanabi is NP-complete, Even for Cheaters who Look at Their Cards

This paper studies a cooperative card game called Hanabi from an algorithmic combinatorial game theory viewpoint. The aim of the game is to play cards from 1 to n in increasing order (this has to be done independently in c different colors). Cards are drawn from a deck one by one. Drawn cards are either immediately played, discarded or stored for future use (overall each player can store up to h cards). The main feature of the game is that players know the cards their partners hold (but not theirs. This information must be shared through hints). We introduce a simplified mathematical model of a single-player version of the game, and show several complexity results: the game is intractable in a general setting even if we forego with the hidden information aspect of the game. On the positive side, the game can be solved in linear time for some interesting restricted cases (i.e., for small values of h and c).

Robust network flow against attackers with knowledge of routing method

Recently, many algorithms are proposed to find a communication flow that is robust against k-edges failures. That flow can be weaker, if attackers can obtain forwarding information in each router. In this paper, we propose an algorithm that find a forwarding algorithm maximizing the remaining flow in that situation. We show that Kishimotos multiroute flow is a (k + 1)-approximation algorithm for the problem, when the route number is k + 1. When the route number is optimally chosen, we show that the multiroute flow is a 2-approximation algorithm for most of randomly generated graphs. Our experimental results show that our algorithm has 15%-37% better performance than max-flow algorithm.

Algorithms for finding robust and sustainable network flows against multilink-attack

This work improves algorithms for finding network flows both sustainable and robust against multilink-attack (MLA). It brings out the relationship between sustainability (flow solution before attack known as MLA-reliable flow) and robustness (flow value after attack known as MLA-robust flow). Both problems are known to be NP-hard. However, exact polynomial time algorithms exist for certain categories of network. It includes the Extended Multiroute Flow (EMRF) algorithm that exhibits a solution to both MLA-robust and MLA-reliable flows. The class of networks solved by EMRF is extended here by using a capacity differentiation method. Although, the previous best-known approximation algorithm to both problems is the naturally robust and sustainable multiroute flow algorithm. A deeper analysis of EMRF an MLA problems leads to new methods to find tighter upper and lower bounds. The success rate of EMRF and the quality of the approximation is evaluated on practical networks as complex networks or grids.

Multiplex flows in citation networks

Knowledge is created and transmitted through generations, and innovation is often seen as a process generated from collective intelligence. There is rising interest in studying how innovation emerges from the blending of accumulated knowledge, and from which path an innovation mostly inherits. A citation network can be seen as a perfect example of one generative process leading to innovation. However, the impact and influence of scientific publication are always difficult to capture and measure. We offer a new take on investigating how the knowledge circulates and is transmitted, inspired by the notion of “stream of knowledge”. We propose to look at this question under the lens of flows in directed acyclic graphs (DAGs). In this framework inspired by the work of Strahler, we can also account for other well known measures of influence such as the h-index. We propose then to analyze flows of influence in a citation networks as an ascending flow. From this point on, we can take a finer look at the diffusion of knowledge through the lens of a multiplex network. In this network, each citation of a specific work constitutes one layer of interaction. Within our framework, we design three measures of multiplex flows in DAGs, namely the aggregated, sum and selective flow, to better understand how citations are influenced. We conduct our experiments with the arXiv HEP-Th dataset, and find insights through the visualization of these multiplex networks.

Bilevel Model for Adaptive Network Flow Problem

Abstract We propose to solve the adaptive network flow problem via a bilevel optimization framework. In this problem, we aim to find a flow that is most robust against any k edges attack. There is an exact algorithm proposed to solve the problem in a specific class of input graphs. However, for some input graphs that are not in that class, a flow obtained from the algorithms is sometimes much less robust than the optimal one. That motivates us to find an efficient exact algorithm based on bilevel optimization framework for the problem in this paper. The framework can give us much better results using reasonable amount of times.

ghost : A Combinatorial Optimization Framework for Real-Time Problems

This paper presents GHOST, a combinatorial optimization framework that a real-time strategy (RTS) AI developer can use to model and solve any problem encoded as a constraint satisfaction/optimization problem (CSP/COP). We show a way to model three different problems as a CSP/COP, using instances from the RTS game StarCraft as test beds. Each problem belongs to a specific level of abstraction (the target selection as reactive control problem, the wall-in as a tactics problem, and the build order planning as a strategy problem). In our experiments, GHOST shows good results computed within some tens of milliseconds. We also show that GHOST outperforms state-of-the-art constraint solvers, matching them on the resources allocation problem, a common combinatorial optimization problem.

Parametric multiroute flow and its application to multilink-attack network

We investigate variants of the max-flow problem in a network under k attacks. The network interdiction problem is to find the minimum max-flow value among (mk) networks that can be obtained by deleting each set of k links. The adaptive network flow problem is to find a flow of the network such that the flow value is maximum against any set of k links attack, when deleting the corresponding flow to those k links in the original flow. First, we prove that max-(k+1)-route flow is a (k+1)-approximation for both problems. Also, we develop a polynomial-time heuristic algorithm for both cases, called the iterative multiroute flow. Then in a second phase, we investigate properties of the function taking the real value h to the max h-route flow value, and apply the result to solve both of the problems. We show that the function is piecewise hyperbolic, and modify a standard parametric optimization technique to find this function. The running time of the algorithm is O(T), when is a sourcesink edge connectivity of our network and T the computation time of a max-flow algorithm. We show that for some instances, when h is optimally chosen, the max- h-route flow is an exact solution for both problems. Maximum multiroute flow algorithm is a (k+1)-approximation algorithm for the network interdiction and adaptive network flow problems.If a parameter of the algorithm is optimally adjusted, the algorithm can be an exact algorithm when the input network satisfies a condition.Experimental results shown that most of the problem instances satisfy the condition.