Recently, we proposed an algorithm for binary tomography based on DC ( difference of convex functions ) programming [13,15]. In this paper, we extend the binary reconstruction problem to multi-valued objects. We describe how such objects can be reconstructed just by combining binary decisions. The proposed algorithm remains practicable for multi-valued reconstructions, and even with a large num...

The Quadratic Convex Reformulation (QCR) method is used to solve quadratic unconstrained binary optimization problems. In this method, the semidefinite relaxation is used to reformulate it to a convex binary quadratic program which is solved using mixed integer quadratic programming solvers. We extend this method to random quadratic unconstrained binary optimization problems. We develop a Penal...

A two-player one-round binary game consists of two cooperative players who each one replies by one bit to a message that receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is called entangled if the players are allowed to share a priori entanglement. It is well-known that the maximum winning probability (the value) of entangled XOR-ga...

Recent advancements in quantum annealing hardware and numerous studies in this area suggests that quantum annealers have the potential to be effective in solving unconstrained binary quadratic programming problems. Naturally, one may desire to expand the application domain of these machines to problems with general discrete variables. In this paper, we explore the possibility of employing quant...

We address a combinatorial optimization problem (COP), namely a particular variant of the matrix chain product problem (MCPP) where the chain involves square dense and triangular matrices. Besides the classical dynamic programming algorithm of cubic complexity, exact greedy algorithms (GA) of linear complexity are also known in the literature. We present in this paper new exact GA’s of linear c...

We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial evaluation cost can be typed, we obtain the core of a functional programming setting for binary field arithmetic with built-in polynomial complexity.

We survey the consecutive-ones property of binary matrices. Herein, a binary matrix has the consecutive-ones property (C1P) if there is a permutation of its columns that places the 1s consecutively in every row. We provide an overview over connections to graph theory, characterizations, recognition algorithms, and applications such as integer linear programming and solving S C.

Topological design of service networks is studied in the paper. A quantitative model and algorithm minimizing cost of processing and delivery are described. An algorithm solving combinatorial problem of optimal design based on binary partitioning, a parametric search and dynamic programming optimization of a binary tree are described and demonstrated in numeric examples.

The approximability of several NP maximization problems is investigated and strong lower bounds for the studied problems are proved. For some of the problems the bounds are the best that can be achieved, unless P = NP. For example we investigate the approximability of Max PB 0 ? 1 Programming, the problem of nding a binary vector x that satisses a set of linear relations such that the objective...

Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...