Related papers: Sorting under Partial Information with Optimal Pre…
Unbreakable decomposition, introduced by Cygan et al. (SICOMP'19) and Cygan et al. (TALG'20), has proven to be one of the most powerful tools for parameterized graph cut problems in recent years. Unfortunately, all known constructions…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…
A partition $(C_1,C_2,...,C_q)$ of $G = (V,E)$ into clusters of strong (respectively, weak) diameter $d$, such that the supergraph obtained by contracting each $C_i$ is $\ell$-colorable is called a strong (resp., weak) $(d,…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
Let F be a set of ordered patterns, i.e., graphs whose vertices are linearly ordered. An F-free ordering of the vertices of a graph H is a linear ordering of V(H) such that none of patterns in F occurs as an induced ordered subgraph. We…
A 1971 conjecture of Graham (later repeated by Erd\H{o}s and Graham) asserts that every set $A \subseteq \mathbb{F}_p \setminus \{0\}$ has an ordering whose partial sums are all distinct. We prove this conjecture for sets of size $|A|…
Selection on $X_1+X_2+\cdots + X_m$ is an important problem with many applications in areas such as max-convolution, max-product Bayesian inference, calculating most probable isotopes, and computing non-parametric test statistics, among…
Motivated by applications in production planning and storage allocation in hierarchical databases, we initiate the study of covering partially ordered items (CPO). Given a capacity $k \in \mathbb{Z}^+$, and a directed graph $G=(V,E)$ where…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
We revisit multipass pairing heaps and path-balanced binary search trees (BSTs), two classical algorithms for data structure maintenance. The pairing heap is a simple and efficient "self-adjusting" heap, introduced in 1986 by Fredman,…
We propose an $O(N\cdot M)$ sorting algorithm by Machine Learning method, which shows a huge potential sorting big data. This sorting algorithm can be applied to parallel sorting and is suitable for GPU or TPU acceleration. Furthermore, we…
Merging $T$ sorted, non-redundant lists containing $M$ elements into a single sorted, non-redundant result of size $N \ge M/T$ is a classic problem typically solved practically in $O(M \log T)$ time with a priority-queue data structure the…
The starting point of this paper is the problem of scheduling $n$ jobs with processing times and due dates on a single machine so as to minimize the total processing time of tardy jobs, i.e., $1||\sum p_j U_j$. This problem was identified…
Enhancing the efficiency of iterative computation on graphs has garnered considerable attention in both industry and academia. Nonetheless, the majority of efforts focus on expediting iterative computation by minimizing the running time per…
Motivated by the desire to cope with data imprecision, we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them. In particular, we…
A run in a string is a maximal periodic substring. For example, the string $\texttt{bananatree}$ contains the runs $\texttt{anana} = (\texttt{an})^{3/2}$ and $\texttt{ee} = \texttt{e}^2$. There are less than $n$ runs in any length-$n$…
Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…
In recent years, questions about the construction of special orderings of a given graph search were studied by several authors. On the one hand, the so called end-vertex problem introduced by Corneil et al. in 2010 asks for search orderings…
The ideas of optimization of learning algorithms in Artificial Neural Networks are reviewed emphasizing generic properties and the online implementations are interpreted from a biological perspective. A simple model of the relevant…