Related papers: Dynamic Programming on Nominal Graphs
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Recent advancements in self-driving car technologies have enabled them to navigate autonomously through various environments. However, one of the critical challenges in autonomous vehicle operation is trajectory planning, especially in…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…
This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation…
Classically, planning tasks are studied as a two-step process: plan creation and plan execution. In situations where plan creation is slow (for example, due to expensive information access or complex constraints), a natural speed-up tactic…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Finding a maximal independent set (MIS) in a graph is a cornerstone task in distributed computing. The local nature of an MIS allows for fast solutions in a static distributed setting, which are logarithmic in the number of nodes or in…
In this paper, we introduce a new model for sublinear algorithms called \emph{dynamic sketching}. In this model, the underlying data is partitioned into a large \emph{static} part and a small \emph{dynamic} part and the goal is to compute a…
How to compute (super) hedging costs in rather general fi- nancial market models with transaction costs in discrete-time ? Despite the huge literature on this topic, most of results are characterizations of the super-hedging prices while it…
The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have…
Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…
Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems,…