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Post training quantization is essential for deploying large language models (LLMs) on resource constrained hardware, yet state of the art methods enforce uniform bit widths across layers, yielding suboptimal accuracy efficiency trade offs.…
The Quadratic Assignment Problem (QAP) is an NP-hard problem which has proven particularly challenging to solve: unlike other combinatorial problems like the traveling salesman problem (TSP), which can be solved to optimality for instances…
One of the most important open problems in machine scheduling is the problem of scheduling a set of jobs on unrelated machines to minimize the makespan. The best known approximation algorithm for this problem guarantees an approximation…
We study a core algorithmic problem in network design called ${F}$-augmentation that involves increasing the connectivity of a given family of cuts ${F}$. Over 30 years ago, Williamson et al. (STOC `93) provided a 2-approximation…
We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous…
We study approximation algorithms for two natural generalizations of the Maximum Quadratic Assignment Problem (MaxQAP). In the Maximum List-Restricted Quadratic Assignment Problem, each node in one partite set may only be matched to nodes…
We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
In the Distance-constrained Vehicle Routing Problem (DVRP), we are given a graph with integer edge weights, a depot, a set of $n$ terminals, and a distance constraint $D$. The goal is to find a minimum number of tours starting and ending at…
Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…
Extensive efforts have been made to boost the performance in the domain of language models by introducing various attention-based transformers. However, the inclusion of linear layers with large dimensions contributes to significant…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…
We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
We study the weighted token swapping problem, in which we are given a graph on $n$ vertices, $n$ weighted tokens, an initial assignment of one token to each vertex, and a final assignment of one token to each vertex. The goal is to find a…
The Steiner Forest problem is an important generalization of the Steiner Tree problem. We are given an undirected graph with nonnegative edge costs and a collection of pairs of vertices. The task is to compute a cheapest forest with the…
This paper presents a novel differentiable method for unstructured weight pruning of deep neural networks. Our learned-threshold pruning (LTP) method learns per-layer thresholds via gradient descent, unlike conventional methods where they…
The random forest (RF) algorithm has become a very popular prediction method for its great flexibility and promising accuracy. In RF, it is conventional to put equal weights on all the base learners (trees) to aggregate their predictions.…