相关论文: Dynamic Ordered Sets with Exponential Search Trees
It is widely assumed that $O(m+\lg \sigma)$ is the best one can do for finding a pattern of length $m$ in a compacted trie storing strings over an alphabet of size $\sigma$, if one insists on linear-size data structures and deterministic…
We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the Line-Leaf Tree, a linear-sized data structure that supports the…
We show how to construct a dynamic ordered dictionary, supporting insert/delete/rank/select on a set of $n$ elements from a universe of size $U$, that achieves the optimal amortized expected time complexity of $O(1 + \log n / \log \log U)$,…
Retrieval data structures are data structures that answer key-value queries without paying the space overhead of explicitly storing keys. The problem can be formulated in four settings (static, value-dynamic, incremental, or dynamic), each…
This paper presents a general technique for optimally transforming any dynamic data structure that operates on atomic and indivisible keys by constant-time comparisons, into a data structure that handles unbounded-length keys whose…
An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…
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…
We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
``Algorithms with predictions'', or ``learning-augmented algorithms'', has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted…
The dynamic optimality conjecture, postulating the existence of an $O(1)$-competitive online algorithm for binary search trees (BSTs), is among the most fundamental open problems in dynamic data structures. Despite extensive work and some…
The representation of a dynamic ordered set of $n$ integer keys drawn from a universe of size $m$ is a fundamental data structuring problem. Many solutions to this problem achieve optimal time but take polynomial space, therefore preserving…
We tackle two long-standing problems related to re-expansions in heuristic search algorithms. For graph search, A* can require $\Omega(2^{n})$ expansions, where $n$ is the number of states within the final $f$ bound. Existing algorithms…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
In this paper we consider the following modification of the iterative search problem. We are given a tree $T$, so that a dynamic catalog $C(v)$ is associated with every tree node $v$. For any $x$ and for any node-to-root path $\pi$ in $T$,…
An algorithm is presented that solves the Minimum Dominating Set problem exactly using polynomial space based on dynamic programming for a tree decomposition. A direct application of dynamic programming based on a tree decomposition would…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
We present a data structure representing a dynamic set S of w-bit integers on a w-bit word RAM. With |S|=n and w > log n and space O(n), we support the following standard operations in O(log n / log w) time: - insert(x) sets S = S + {x}. -…
We present a study of several generic tree search techniques applied to the Sequential Ordering Problem. This study enables us to propose a simple and competitive tree search algorithm. It consists of an iterative Beam Search algorithm that…
Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…
The need for scalable concurrent ordered set data structures with linearizable range query support is increasing due to the rise of multicore computers, data processing platforms and in-memory databases. This paper presents a new concurrent…