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Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
We give one more proof of the first linear programming bound for binary codes, following the line of work initiated by Friedman and Tillich. The new argument is somewhat similar to previous proofs, but we believe it to be both simpler and…
Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot…
We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct…
In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…
It is well known that we can use structural proof theory to refine, or generalize, existing paradigmatic computational primitives, or to discover new ones. Under such a point of view we keep developing a programme whose goal is establishing…
It is well known that, given \(b\ge 0\), finding an $(a,b)$-trapping set with the minimum \(a\) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…
Warehouses are nowadays the scene of complex logistic problems integrating different decision layers. This paper addresses the Joint Order Batching, Picker Routing and Sequencing Problem with Deadlines (JOBPRSP-D) in rectangular warehouses.…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of…
In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique…
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
Timeline-based planning is an approach originally developed in the context of space mission planning and scheduling, where problem domains are modelled as systems made of a number of independent but interacting components, whose behaviour…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
We consider a distribution logistics scenario where a shipping operator, managing a limited amount of resources, receives a stream of collection requests, issued by a set of customers along a booking time-horizon, that are referred to a…
A fundamental problem in data management is to find the elements in an array that match a query. Recently, learned indexes are being extensively used to solve this problem, where they learn a model to predict the location of the items in…