Related papers: A faster algorithm for the construction of optimal…
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…
The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the…
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the…
In the paper, we focus on complexity of C5.0 algorithm for constructing decision tree classifier that is the models for the classification problem from machine learning. In classical case the decision tree is constructed in $O(hd(NM+N \log…
In 2013, Orlin proved that the max flow problem could be solved in $O(nm)$ time. His algorithm ran in $O(nm + m^{1.94})$ time, which was the fastest for graphs with fewer than $n^{1.06}$ arcs. If the graph was not sufficiently sparse, the…
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 focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique…
In the first part of the paper, we present an (1+\mu)-approximation algorithm to the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and the lines. The…
Depth first search (DFS) tree is one of the most well-known data structures for designing efficient graph algorithms. Given an undirected graph $G=(V,E)$ with $n$ vertices and $m$ edges, the textbook algorithm takes $O(n+m)$ time to…
We consider the numerical taxonomy problem of fitting a positive distance function ${D:{S\choose 2}\rightarrow \mathbb R_{>0}}$ by a tree metric. We want a tree $T$ with positive edge weights and including $S$ among the vertices so that…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
The circuit-level implementation of a quantum string-matching algorithm, which matches a search string (pattern) of length $M$ inside a longer text of length $N$, has already been demonstrated in the literature to outperform its classical…
The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the edit-distance between…
In this paper, we study the problem of finding an integral multiflow which maximizes the sum of flow values between every two terminals in an undirected tree with a nonnegative integer edge capacity and a set of terminals. In general, it is…
We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had…
The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper,…
A closed string $u$ is either of length one or contains a border that occurs only as a prefix and as a suffix in $u$ and nowhere else within $u$. In this paper, we present fast $\mathcal{O}(n\log n)$ time algorithms to compute all…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…