相关论文: Data Structures for Mergeable Trees
In this paper we describe a dynamic data structure that answers one-dimensional stabbing-max queries in optimal $O(\log n/\log\log n)$ time. Our data structure uses linear space and supports insertions and deletions in $O(\log n)$ and…
We present a deterministic fully-dynamic data structure for maintaining information about the bridges in a graph. We support updates in $\tilde{O}((\log n)^2)$ amortized time, and can find a bridge in the component of any given vertex, or a…
Classic dynamic data structure problems maintain a data structure subject to a sequence S of updates and they answer queries using the latest version of the data structure, i.e., the data structure after processing the whole sequence. To…
Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…
This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the…
We present a randomized algorithm for reconstructing directed rooted trees of $n$ nodes and node degree at most $d$, by asking at most $O(dn\log^2 n)$ path queries. Each path query takes as input an origin node and a target node, and…
We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of…
Dynamic programming is widely used for exact computations based on tree decompositions of graphs. However, the space complexity is usually exponential in the treewidth. We study the problem of designing efficient dynamic programming…
The dynamic trees problem is to maintain a tree under edge updates while supporting queries like connectivity queries or path queries. Despite the first data structure for this fundamental problem -- the link-cut tree -- being invented 40…
The task of accumulating a portion of a list of values, whose values may be updated at any time, is widely used throughout various applications in computer science. While it is trivial to accomplish this task without any constraints,…
We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We investigate the limits of one of the fundamental ideas in data structures: fractional cascading. This is an important data structure technique to speed up repeated searches for the same key in multiple lists and it has numerous…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
We consider the problem of enumerating, for a given directed graph $G=(V,E)$ and a node $r\in V$, all directed spanning trees of $G$ rooted at $r$. For undirected graphs, the corresponding problem of enumerating all spanning trees has…
We give improved algorithms for maintaining edge-orientations of a fully-dynamic graph, such that the out-degree of each vertex is bounded. On one hand, we show how to orient the edges such that the out-degree of each vertex is proportional…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…