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Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…
Given a graph G, a matching is a subset of edges of G that do not share an endpoint. A matching M is uniquely restricted if the subgraph induced by the endpoints of the edges of M has exactly one perfect matching. Given a graph G and a…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
Iterative pruning is one of the most effective compression methods for pre-trained language models. We discovered that finding the optimal pruning decision is an equality-constrained 0-1 Integer Linear Programming problem. The solution to…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
We study the linearizability monitoring problem, which asks whether a given concurrent history of a data structure is equivalent to some sequential execution of the same data structure. In general, this problem is $\textsf{NP}$-hard, even…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…
Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
An intensive line of research on fixed parameter tractability of integer programming is focused on exploiting the relation between the sparsity of a constraint matrix $A$ and the norm of the elements of its Graver basis. In particular,…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing $W[1]$-hardness proofs for these problems, since XNLP-hardness implies $W[t]$-hardness for…
Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete…