Related papers: Algorithms for Cut Problems on Trees
In the $k$-cut problem, we want to find the lowest-weight set of edges whose deletion breaks a given (multi)graph into $k$ connected components. Algorithms of Karger \& Stein can solve this in roughly $O(n^{2k})$ time. On the other hand,…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut above the Edwards-Erd\H{o}s bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices…
We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…
It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the…
The tree edit distance problem is a natural generalization of the classic string edit distance problem. Given two ordered, edge-labeled trees $T_1$ and $T_2$, the edit distance between $T_1$ and $T_2$ is defined as the minimum total cost of…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
This paper presents a parallel solution based on the coarse-grained multicomputer (CGM) model using the four-splitting technique to solve the optimal binary search tree problem. The well-known sequential algorithm of Knuth solves this…
In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of finding an optimal binary search tree. Knuth's algorithm works only for search trees based on 3-way comparisons, while most modern computers support only 2-way…
We give an $n^{O(\log\log n)}$-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over $\{\pm 1\}^n$. Even in the realizable setting, the previous fastest runtime was…
We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to…
In a graph, a perfect matching cut is an edge cut that is a perfect matching. Perfect Matching Cut (PMC) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and…
The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
The (unweighted) tree edit distance problem for $n$ node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in $O(n ^ 3)$ time [Demaine,…
The fundamental sparsest cut problem takes as input a graph $G$ together with the edge costs and demands, and seeks a cut that minimizes the ratio between the costs and demands across the cuts. For $n$-node graphs~$G$ of treewidth~$k$,…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…