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In the decision tree computation model for Boolean functions, the depth corresponds to query complexity, and size corresponds to storage space. The depth measure is the most well-studied one, and is known to be polynomially related to…
We introduce the Thresholding Monte Carlo Tree Search problem, in which, given a tree $\mathcal{T}$ and a threshold $\theta$, a player must answer whether the root node value of $\mathcal{T}$ is at least $\theta$ or not. In the given tree,…
In the laminar-constrained spanning tree problem, the goal is to find a minimum-cost spanning tree which respects upper bounds on the number of times each cut in a given laminar family is crossed. This generalizes the well-studied…
We study fundamental block-structured integer programs called tree-fold and multi-stage IPs. Tree-fold IPs admit a constraint matrix with independent blocks linked together by few constraints in a recursive pattern; and transposing their…
We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…
Optimizing data movements during program executions is essential for achieving high performance in modern computing systems. This has been classically modeled with the Red-Blue Pebble Game and its variants. In existing models, it is…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of Mixed-Integer Programming solvers. In its full form, SB evaluates all variables to branch on and…
In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
Given a tree $T$ on $n$ vertices, and $k, b, s_1, \ldots, s_b \in N$, the Tree Partitioning problem asks if at most $k$ edges can be removed from $T$ so that the resulting components can be grouped into $b$ groups such that the number of…
An adaptive regularization algorithm using high-order models is proposed for partially separable convexly constrained nonlinear optimization problems whose objective function contains non-Lipschitzian $\ell_q$-norm regularization terms for…
Avraham et al. [AFK+15] presented an alternative approach to parametric search, called \emph{bifurcation}, that performs faster under certain circumstances. Intuitively, when the underlying decider execution can be rolled back cheaply and…
There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
The embedding-based representation learning is commonly used in deep learning recommendation models to map the raw sparse features to dense vectors. The traditional embedding manner that assigns a uniform size to all features has two…
We revisit the \textsc{$k$-Secluded Tree} problem. Given a vertex-weighted undirected graph $G$, its objective is to find a maximum-weight induced subtree $T$ whose open neighborhood has size at most $k$. We present a fixed-parameter…
We investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
We show that the class of strongly connected graphical models with treewidth at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]),…