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The Detection Transformer (DETR), by incorporating the Hungarian algorithm, has significantly simplified the matching process in object detection tasks. This algorithm facilitates optimal one-to-one matching of predicted bounding boxes to…
Deletion problems are those where given a graph $G$ and a graph property $\pi$, the goal is to find a subset of edges such that after its removal the graph $G$ will satisfy the property $\pi$. Typically, we want to minimize the number of…
Phylogenetic networks are a flexible model of evolution that can represent reticulate evolution and handle complex data. Tree-based networks, which are phylogenetic networks that have a spanning tree with the same root and leaf-set as the…
Solving (mixed) integer linear programs, (M)ILPs for short, is a fundamental optimization task. While hard in general, recent years have brought about vast progress for solving structurally restricted, (non-mixed) ILPs: $n$-fold, tree-fold,…
Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…
Fragment-Based Drug Discovery (FBDD) is a popular approach in early drug development, but designing effective linkers to combine disconnected molecular fragments into chemically and pharmacologically viable candidates remains challenging.…
Artificial intelligence applications in autonomous driving, medical diagnostics, and financial systems increasingly demand machine learning models that can provide robust uncertainty quantification, interpretability, and noise resilience.…
Integer programming (IP) is an important and challenging problem. Approximate methods have shown promising performance on both effectiveness and efficiency for solving the IP problem. However, we observed that a large fraction of variables…
We introduce the tree-decomposition-based parameter totally $\Delta$-modular treewidth (TDM-treewidth) for matrices with two nonzero entries per row. We show how to solve integer programs whose matrices have bounded TDM-treewidth in…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
This paper studies an accelerated fitted value iteration (FVI) algorithm to solve high-dimensional Markov decision processes (MDPs). FVI is an approximate dynamic programming algorithm that has desirable theoretical properties. However, it…
The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…
To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence…
In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an elementary approach: we reformulate any semidefinite…