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Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min,…
We improve complexity bounds for energy-efficient speed scheduling problems for both the single processor and multi-processor cases. Energy conservation has become a major concern, so revisiting traditional scheduling problems to take into…
In this paper, we develop new algorithms for the basic RNA folding problem. Given an RNA sequence that contains $n$ nucleotides, the goal of the problem is to compute a pseudoknot-free secondary structure that maximizes the number of base…
Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…
Given an array of distinct integers $A[1\ldots n]$, the Range Minimum Query (RMQ) problem requires us to construct a data structure from $A$, supporting the RMQ query: given an interval $[a,b]\subseteq[1,n]$, return the index of the minimum…
Bille and G{\o}rtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string $S$ of $n$ characters with integer labels in ([0, u]), such that later, given an interval ([a, b]) and…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
We consider the task of assigning unique integers to a group of processes in an asynchronous distributed system of a total of $n$ processes prone to crashes that communicate through shared read-write registers. In the Renaming problem, an…
In the classical longest palindromic substring (LPS) problem, we are given a string $S$ of length $n$, and the task is to output a longest palindromic substring in $S$. Gilbert, Hajiaghayi, Saleh, and Seddighin [SPAA 2023] showed how to…
Bounding the queue length in a multiserver queue is a central challenge in queueing theory. Even for the classical $G/G/n$ queue with homogeneous servers, it is highly non-trivial to derive a simple and accurate bound for the steady-state…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
We revisit Hopcroft's problem and related fundamental problems about geometric range searching. Given $n$ points and $n$ lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line…
Solving linear systems and quadratic programming (QP) problems are both ubiquitous tasks in the engineering and computing fields. Direct methods for solving systems, such as Cholesky, LU, and QR factorizations, exhibit data-independent time…
The NP-hard problem of task scheduling with communication delays (P|prec,c_{ij}|C_{\mathrm{max}}) is often tackled using approximate methods, but guarantees on the quality of these heuristic solutions are hard to come by. Optimal schedules…
In this paper, we first consider the subpath convex hull query problem: Given a simple path $\pi$ of $n$ vertices, preprocess it so that the convex hull of any query subpath of $\pi$ can be quickly obtained. Previously, Guibas, Hershberger,…
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights and characterization for different iterative process, and…
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with $n$ items using $O^*(2^{0.86n})$ time and polynomial space, where the $O^*(\cdot)$ notation suppresses factors polynomial in the input size.…
We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\times n$ together with a vector $b\in \mathbb{R}^m$ are streamed to us…
We propose algorithms that, given the input string of length $n$ over integer alphabet of size $\sigma$, construct the Burrows-Wheeler transform (BWT), the permuted longest-common-prefix (PLCP) array, and the LZ77 parsing in…