Related papers: Strong Steiner Tree Approximations in Practice
In the longest plane spanning tree problem, we are given a finite planar point set $\mathcal{P}$, and our task is to find a plane (i.e., noncrossing) spanning tree for $\mathcal{P}$ with maximum total Euclidean edge length. Despite more…
In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…
The Weighted Tree Augmentation Problem (WTAP) is a fundamental network design problem where the goal is to find a minimum-cost set of additional edges (links) to make an input tree 2-edge-connected. While a 2-approximation is standard and…
We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2-1/(n-1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n^3 log n) time. it applies the…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
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…
In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…
Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…
In the design of greedy algorithms for the maximum cardinality matching problem the utilization of degree information when selecting the next edge is a well established and successful approach. We define the class of "degree sensitive"…
In the $k$-connected directed Steiner tree problem ($k$-DST), we are given an $n$-vertex directed graph $G=(V,E)$ with edge costs, a connectivity requirement $k$, a root $r\in V$ and a set of terminals $T\subseteq V$. The goal is to find a…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…
Replicability is a fundamental challenge in reinforcement learning (RL), as RL algorithms are empirically observed to be unstable and sensitive to variations in training conditions. To formally address this issue, we study \emph{list…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
Binary search trees (BSTs) are one of the most basic and widely used data structures. The best static tree for serving a sequence of queries (searches) can be computed by dynamic programming. In contrast, when the BSTs are allowed to be…
We consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Consider a graph with n nodes and m edges, independent edge weights and lengths, and arbitrary distance demands for node pairs. The spanner problem asks for a minimum-weight subgraph that satisfies these demands via sufficiently short paths…