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We present $k^{O(k^2)} m$ time algorithms for various problems about decomposing a given undirected graph by edge cuts or vertex separators of size $<k$ into parts that are ``well-connected'' with respect to cuts or separators of size $<k$;…
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…
A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root…
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
The shortest path (SP) and shortest paths tree (SPT) problems arise both as direct applications and as subroutines of overlay algorithms solving more complex problems such as the constrained shortest path (CSP) or the constrained minimum…
The paper presents the first \emph{concurrency-optimal} implementation of a binary search tree (BST). The implementation, based on a standard sequential implementation of an internal tree, ensures that every \emph{schedule} is accepted,…
The access lemma (Sleator and Tarjan, JACM 1985) is a property of binary search trees that implies interesting consequences such as static optimality, static finger, and working set property. However, there are known corollaries of the…
The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…
Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph $G=(V, E)$ with edge costs $c \in \mathbb{R}_{\geq 0}^E$, a root $r \in V$ and $k$ terminals $K\subseteq…
We present an approach to implement binary search trees in the rule-based graph programming language GP 2. Our implementation uses GP 2's rooted graph transformation rules to be fast and supports insertion, deletion and query operations. We…
Datacenter networks are becoming increasingly flexible with the incorporation of new networking technologies, such as optical circuit switches. These technologies allow for programmable network topologies that can be reconfigured to better…
Consider the task of performing a sequence of searches in a binary search tree. After each search, we allow an algorithm to arbitrarily restructure the tree. The cost of executing the task is the sum of the time spent searching and the time…
Decision Tree is a classic formulation of active learning: given $n$ hypotheses with nonnegative weights summing to 1 and a set of tests that each partition the hypotheses, output a decision tree using the provided tests that uniquely…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
Computing bounded depth decompositions is a bottleneck in many applications of the treedepth parameter. The fastest known algorithm, which is due to Reidl, Rossmanith, S\'{a}nchez Villaamil, and Sikdar [ICALP 2014], runs in…
In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
The independence number of a tree decomposition is the size of a largest independent set contained in a single bag. The tree-independence number of a graph $G$ is the minimum independence number of a tree decomposition of $G$. As shown…
This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest…