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Hirschberg's algorithm (1975) reduces the space complexity for the longest common subsequence problem from $O(N^2)$ to $O(N)$ via recursive midpoint bisection on a grid dynamic program (DP). We show that the underlying idea generalizes to a…
This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…
We study variants of the mean problem under the $p$-Dynamic Time Warping ($p$-DTW) distance, a popular and robust distance measure for sequential data. In our setting we are given a set of finite point sequences over an arbitrary metric…
Huffman compression is a statistical, lossless, data compression algorithm that compresses data by assigning variable length codes to symbols, with the more frequently appearing symbols given shorter codes than the less. This work is a…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for…
AIFV-$2$ codes are a new method for constructing lossless codes for memoryless sources that provide better worst-case redundancy than Huffman codes. They do this by using two code trees instead of one and also allowing some bounded delay in…
Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
Slowly changing variables in a continuous state space constitute an important category of reinforcement learning and see its application in many domains, such as modeling a climate control system where temperature, humidity, etc. change…
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
Huffman Compression, also known as Huffman Coding, is one of many compression techniques in use today. The two important features of Huffman coding are instantaneousness that is the codes can be interpreted as soon as they are received and…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not…
Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field…
Recent advances in Deep Neural Networks (DNNs) have led to active development of specialized DNN accelerators, many of which feature a large number of processing elements laid out spatially, together with a multi-level memory hierarchy and…
Dynamic time warping distance (DTW) is a widely used distance measure between time series. The best known algorithms for computing DTW run in near quadratic time, and conditional lower bounds prohibit the existence of significantly faster…
A large number of NP-hard graph problems can be solved in $f(w)n^{O(1)}$ time and space when the input graph is provided together with a tree decomposition of width $w$, in many cases with a modest exponential dependence $f(w)$ on $w$.…