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We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
We study the general norm optimization for combinatorial problems, initiated by Chakrabarty and Swamy (STOC 2019). We propose a general formulation that captures a large class of combinatorial structures: we are given a set $U$ of $n$…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…
Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large…
In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. programming problem. The developed algorithm is a branch-and-bound-based algorithm…
Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…
We consider approximation algorithms for the problem of finding $x$ of minimal norm $\|x\|$ satisfying a linear system $\mathbf{A} x = \mathbf{b}$, where the norm $\|\cdot \|$ is arbitrary and generally non-Euclidean. We show a simple…
This paper considers an opportunistic scheduling problem over a renewal system. A controller observes a random event at the beginning of each renewal frame and then chooses an action in response to the event, which affects the duration of…
Traditional lock-free parallel algorithms for combinatorial optimization problems, such as shortest paths, stable matching, and job scheduling require programmers to write problem-specific routines and synchronization code. We propose a…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…
This study explores the throughput and delay that can be achieved by various forwarding schemes employing multiple paths and different degrees of redundancy focusing on linear network coding. The key contribution of the study is an…
In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding…
In this paper we consider the class of anti-uniform Huffman codes and derive tight lower and upper bounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. The Fibonacci distributions…
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…