Related papers: SAT encodings for sorting networks, single-excepti…
The at-most-k constraint is ubiquitous in combinatorial problems, and numerous SAT encodings are available for the constraint. Prior experiments have shown the competitiveness of the sequential-counter encoding for k $>$ 1, and have…
Random linear network coding is a particularly decentralized approach to the multicast problem. Use of random network codes introduces a non-zero probability however that some sinks will not be able to successfully decode the required…
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…
This paper shows an application of the theory of sorting networks to facilitate the synthesis of optimized general purpose sorting libraries. Standard sorting libraries are often based on combinations of the classic Quicksort algorithm with…
In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity order or the transmission rate…
When solving a combinatorial problem using propositional satisfiability (SAT), the encoding of the problem is of vital importance. We study encodings of Pseudo-Boolean (PB) constraints, a common type of arithmetic constraint that appears in…
Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. That is why a lot of effort has been put into finding sorting algorithms that sort large sets as fast as possible. But the…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
The poset cover problem seeks a minimum set of partial orders whose linear extensions cover a given set of linear orders. Recognizing its NP-completeness, we devised a non-trivial reduction to the Boolean satisfiability problem using a…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
In the field of Boolean satisfiability problems (SAT), at-most-k constraints, which suppress the number of true target variables at most k, are often used to describe objective problems. At-most-k constraints are used not only for…
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
In this paper we investigate how to estimate the hardness of Boolean satisfiability (SAT) encodings for the Logical Equivalence Checking problem (LEC). Meaningful estimates of hardness are important in cases when a conventional SAT solver…
Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt to random fluctuations in the number of erasures in individual batches, it is not optimal to recode and…
We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes…
Decision lists are one of the most easily explainable machine learning models. Given the renewed emphasis on explainable machine learning decisions, this machine learning model is increasingly attractive, combining small size and clear…
A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n->infinity the space-time process of swaps converges to the…
We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…