相关论文: Some New Methods to Generate Short Addition Chains
Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…
We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…
Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
In pursuit of higher energy efficiency in computer networks, one subfield of green traffic engineering aims at reducing the size of a network during times of low traffic, while still guaranteeing the ability to route all occurring demands.…
Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable…
In an undirected graph, a $k$-cut is a set of edges whose removal breaks the graph into at least $k$ connected components. The minimum weight $k$-cut can be computed in $O(n^{O(k)})$ time, but when $k$ is treated as part of the input,…
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,…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the…
"Addition-by-subtraction" coupled cluster (CC) approaches provide a promising approach to treating the difficult strong correlation problem by simplifying the standard CC equations. In a separate vein, linearized CC methods have drawn…
Efficient scalar multiplication is critical for enhancing the performance of elliptic curve cryptography (ECC), especially in applications requiring large-scale or real-time cryptographic operations. This paper proposes an M-ary…
Spanner constructions focus on the initial design of the network. However, networks tend to improve over time. In this paper, we focus on the improvement step. Given a graph and a budget $k$, which $k$ edges do we add to the graph to…
A major challenge in next-generation genome sequencing (NGS) is to assemble massive overlapping short reads that are randomly sampled from DNA fragments. To complete assembling, one needs to finish a fundamental task in many leading…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
Minimizing the weight of an edge set satisfying parity constraints is a challenging branch of combinatorial optimization as witnessed by the binary hypergraph chapter of Alexander Schrijver's book ``Combinatorial Optimization" (Chapter 80).…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…
Cross-validation is a useful and generally applicable technique often employed in machine learning, including decision tree induction. An important disadvantage of straightforward implementation of the technique is its computational…
Augmentative and Alternative Communication (AAC) systems allow people with disabilities to provide input to devices which empower them to more fully interact with their environment. Within AAC, switch scanning is a common paradigm for…