Related papers: Bitwise operations related to a combinatorial prob…
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search.…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices…
We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
An algorithm for obtaining all n\times n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has…
We study equivalence determination of unitary operations, a task analogous to quantum state discrimination. The candidate states are replaced by unitary operations given as a quantum sample, i.e., a black-box device implementing a candidate…
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…
Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
Binary, or one-bit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this work, we study the problem of data classification from binary data and…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the binary case is thus the first nontrivial case. This paper sees…
Tackling binary program analysis problems has traditionally implied manually defining rules and heuristics, a tedious and time-consuming task for human analysts. In order to improve automation and scalability, we propose an alternative…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
The binary string matching problem consists in finding all the occurrences of a pattern in a text where both strings are built on a binary alphabet. This is an interesting problem in computer science, since binary data are omnipresent in…
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…