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A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
The robust adaptive beamforming (RAB) problem is considered via the worst-case signal-to-interference-plus-noise ratio (SINR) maximization over distributional uncertainty sets for the random interference-plus-noise covariance (INC) matrix…
Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion…
The max-cut problem is a classical graph theory problem which is NP-complete. The best polynomial time approximation scheme relies on \emph{semidefinite programming} (SDP). We study the conditions under which graphs of certain classes have…
Answer Set Programming (ASP) is a problem modeling and solving framework for several problems in KR with growing industrial applications. Also for studies of computational complexity and deeper insights into the hardness and its sources,…
We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of…
Answer Set Programming (ASP) is a paradigm for modeling and solving problems for knowledge representation and reasoning. There are plenty of results dedicated to studying the hardness of (fragments of) ASP. So far, these studies resulted in…
Given a simple undirected graph $G$, the maximum $k$-club problem is to find a maximum-cardinality subset of nodes inducing a subgraph of diameter at most $k$ in $G$. This NP-hard generalization of clique, originally introduced to model low…
Constrained Stochastic Shortest Path Problems (CSSPs) model problems with probabilistic effects, where a primary cost is minimised subject to constraints over secondary costs, e.g., minimise time subject to monetary budget. Current…
For the minimum cardinality vertex cover and maximum cardinality matching problems, the max-product form of belief propagation (BP) is known to perform poorly on general graphs. In this paper, we present an iterative loopy annealing BP…
We study practical approaches to solving the token swapping (TSWAP) problem optimally in this short paper. In TSWAP, we are given an undirected graph with colored vertices. A colored token is placed in each vertex. A pair of tokens can be…
The GC problem is to identify a pre-determined number of center vertices such that the distances or costs from (or to) the centers to (or from) other vertices is minimized. The bottleneck of a path is the minimum capacity of edges on the…
In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical…
A variant of the well-known Shortest Path Problem is studied in this paper, where pairs of conflicting arcs are provided, and for each conflicting pair a penalty is paid once neither or both of the arcs are selected. This configures a set…
Cutwidth is a widely studied parameter that quantifies how well a graph can be decomposed along small edge-cuts. It complements pathwidth, which captures decomposition by small vertex separators, and it is well-known that cutwidth…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
We introduce novel methods for encoding acyclicity and s-t-reachability constraints for propositional formulas with underlying directed graphs. They are based on vertex elimination graphs, which makes them suitable for cases where the…
We introduce a variant of the graph coloring problem, which we denote as {\sc Budgeted Coloring Problem} (\bcp). Given a graph $G$, an integer $c$ and an ordered list of integers $\{b_1, b_2, \ldots, b_c\}$, \bcp asks whether there exists a…
The existing inverse power ($\mathbf{IP}$) method for solving the balanced graph cut lacks local convergence and its inner subproblem requires a nonsmooth convex solver. To address these issues, we develop a simple inverse power…