Multi-robot task allocation for safe planning under dynamic uncertainties

This paper considers the problem of multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control policy is challenging not only because of the complexity of incorporating dynamic uncertainties while planning, but also because of the exponential growth in problem size as a function of the number of robots. Leveraging recent works obtaining a tractable safety maximizing plan for a single robot, we propose a scalable two-stage framework to solve the problem at hand. Specifically, the problem is split into a low-level single-agent planning problem and a high-level task allocation problem. The low-level problem uses an efficient approximation of stochastic reachability for a Markov decision process to handle the dynamic uncertainty. The task allocation, on the other hand, is solved using polynomial-time forward and reverse greedy heuristics. The safety objective of our multi-robot safe planning problem allows an implementation of the greedy heuristics through a distributed auction-based approach. Moreover, by leveraging the properties of the safety objective function, we ensure provable performance bounds on the safety of the approximate solutions proposed by these two heuristics. Our result is illustrated through case studies

Discovering Reliable Dependencies from Data: Hardness and Improved Algorithms

The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We show that the problem is NP-hard, which justifies the usage of worst-case exponential-time as well as heuristic search methods. We then substantially improve the practical performance for both optimization styles by deriving a novel admissible bounding function that has an unbounded potential for additional pruning over the previously proposed one. Finally, we empirically investigate the approximation ratio of the greedy algorithm and show that it produces highly competitive results in a fraction of time needed for complete branch-and-bound style search.Comment: Accepted to Proceedings of the IEEE International Conference on Data Mining (ICDM'18

Complexity, Algorithms, and Heuristics of Influence Maximization

People often adopt improved behaviors, products, or ideas through the influence of friends. This is modeled by emph{cascades}. One way to spread such positive elements through society is to identify those most influential agents---those that cause the maximum spread, and initiate the spread by seeding them. However, this strategy has a key difficulty: finding these influential seed nodes. This is difficult even if both the network structure and the way the cascade spreads are known. In emph{the influence maximization problem}, a central planner is given a graph and a limited budget $k$, and he needs to pick $k$ seeds such that the expected total number of infected vertices in the graph at the end of the cascade is maximized. This problem plays a central role in viral marketing, outbreak detection, rumor controls, etc. This thesis focuses on computational complexity, approximability and algorithm/heuristic design aspects of the influence maximization problem, with both emph{submodular} and emph{nonsubmodular} diffusion models. The first part of the thesis studies submodular influence maximization mainly in the computational complexity and algorithm analysis aspects, which includes some breakthroughs in understanding the approximability of submodular influence maximization and the theoretical performance of the well-studied greedy algorithm. The second part of the thesis focuses on nonsubmodular influence maximization. New sociologically founded nonsubmodular diffusion models are proposed, and we show how the seeding strategy for nonsubmodular diffusion models is fundamentally different compared to submodular diffusion models.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155221/1/bstao_1.pd

Improved Approximation Algorithm for Minimum-Weight (1,m)(1,m)--Connected Dominating Set

The classical minimum connected dominating set (MinCDS) problem aims to find a minimum-size subset of connected nodes in a network such that every other node has at least one neighbor in the subset. This problem is drawing considerable attention in the field of wireless sensor networks because connected dominating sets can serve as virtual backbones of such networks. Considering fault-tolerance, researchers developed the minimum $k$-connected $m$-fold CDS (Min$(k,m)$CDS) problem. Many studies have been conducted on MinCDSs, especially those in unit disk graphs. However, for the minimum-weight CDS (MinWCDS) problem in general graphs, algorithms with guaranteed approximation ratios are rare. Guha and Khuller designed a $(1.35+\varepsilon)\ln n$-approximation algorithm for MinWCDS, where $n$ is the number of nodes. In this paper, we improved the approximation ratio to $2H(\delta_{\max}+m-1)$ for MinW$(1,m)$CDS, where $\delta_{\max}$ is the maximum degree of the graph

Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of our algorithms is much less than [30], and our algorithms can be used to efficiently minimize a difference between submodular functions under various combinatorial constraints, a problem not previously addressed. We provide computational bounds and a hardness result on the mul- tiplicative inapproximability of minimizing the difference between submodular functions. We show, however, that it is possible to give worst-case additive bounds by providing a polynomial time computable lower-bound on the minima. Finally we show how a number of machine learning problems can be modeled as minimizing the difference between submodular functions. We experimentally show the validity of our algorithms by testing them on the problem of feature selection with submodular cost features.Comment: 17 pages, 8 figures. A shorter version of this appeared in Proc. Uncertainty in Artificial Intelligence (UAI), Catalina Islands, 201

Etude de la Maximisation de l'Influence dans les Réseaux Sociaux

National audienceInfluence maximization is a NP-hard problem depending on the diffusion of information in social networks. The Greedy hill climbing algorithm have been proved a good approximation if the influence fonction we try to optimize is submodular, which is the case for standard diffusion models.We present a diffusion model not equivalent to standard models for which the influence function is not submodular. Then we propose, using toy graphs and a real social network, a study of different influence maximization algorithms on this model and on the standard model IC: some basic heuristics, the greedy hill climbing method, a generalization of the greedy method and an optimization method for submodular functions. We show that even if the influence function is not submodular, the greedy algorithm obtain good results while being able to scale efficiently