相关论文: General Policies, Subgoal Structure, and Planning …
Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we…
We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known -- e.g.~[Fischer,…
The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity…
We give alternative definitions for maximum matching width, e.g. a graph $G$ has $\operatorname{mmw}(G) \leq k$ if and only if it is a subgraph of a chordal graph $H$ and for every maximal clique $X$ of $H$ there exists $A,B,C \subseteq X$…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an…
A generalized criterion for signature-based algorithms to compute Gr\"obner bases is proposed in this paper. This criterion is named by "generalized criterion", because it can be specialized to almost all existing criteria for…
The network-based study of financial systems has received considerable attention in recent years but has seldom explicitly incorporated the dynamic aspects of such systems. We consider this problem setting from the temporal point of view…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
Partial differential equation (PDE) constrained optimization problems such as seismic full waveform inversion (FWI) frequently arise in the geoscience and related fields. For such problems, many observations are usually gathered by multiple…
Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been…
Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
We present the first fixed-parameter tractable (FPT) algorithms for exact computation of generalized hypertree width (ghw) and fractional hypertree width (fhw). Our algorithms are parameterized by the target width, the rank, and the maximum…
The goal of dynamic time warping is to transform or warp time in order to approximately align two signals together. We pose the choice of warping function as an optimization problem with several terms in the objective. The first term…
A set S of vertices of a graph is a defensive alliance if, for each element of S, the majority of its neighbors is in S. The problem of finding a defensive alliance of minimum size in a given graph is NP-hard and there are polynomial-time…
We are witnessing an increasing use of data-driven predictive models to inform decisions. As decisions have implications for individuals and society, there is increasing pressure on decision makers to be transparent about their decision…
This thesis is concerned with continuous, static, and single-objective optimization problems subject to inequality constraints. Nevertheless, some methods to handle other kinds of problems are briefly reviewed. The particle swarm…
FWI seeks to achieve a high-resolution model of the subsurface through the application of multi-variate optimization to the seismic inverse problem. Although now a mature technology, FWI has limitations related to the choice of the…