相关论文: Should Static Search Trees Ever Be Unbalanced?
We present an extension of Monte Carlo Tree Search (MCTS) that strongly increases its efficiency for trees with asymmetry and/or loops. Asymmetric termination of search trees introduces a type of uncertainty for which the standard upper…
We revisit weight-balanced trees, also known as trees of bounded balance. This class of binary search trees was invented by Nievergelt and Reingold in 1972. Such trees are obtained by assigning a weight to each node and requesting that the…
We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…
We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as…
Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
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…
A graph G is called well-indumatched if all of its maximal induced matchings have the same size. In this paper we characterize all well-indumatched trees. We provide a linear time algorithm to decide if a tree is well-indumatched or not.…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for…
We solve a class of optimization problems for (phylogenetic) $X$-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so…
In this paper we design and prove correct a fully dynamic distributed algorithm for maintaining an approximate Steiner tree that connects via a minimum-weight spanning tree a subset of nodes of a network (referred as Steiner members or…
We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…
We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…
Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…
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…
We consider the problem of computing optimal search trees on trees (STTs). STTs generalize binary search trees (BSTs) in which we search nodes in a path (linear order) to search trees that facilitate search over general tree topologies.…
In this paper, we provide algorithms to rank and unrank certain degree-restricted classes of Cayley trees (spanning trees of the n-vertex complete graph). Specifically, we consider classes of trees that have a given set of leaves or a fixed…
We consider a combinatorial question about searching for an unknown ideal $\mu$ within a known pointed poset $\lambda$. Elements of $\lambda$ may be queried for membership in $\mu$, but at most $k$ positive queries are permitted. We provide…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…