A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their corresponding primal edges. The problem of constructing such drawings has a long tradition when the drawings of both primal and dual are required to be straight-...

We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm, and then transforming it into a primal-dual algorithm. This was done in the case of the 2-approximation algorithms for the f...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗(κ) linear complementarity problems (LCPs). We generalize the analysis of BER’s primal-dual interior point algorithm for LP to P∗(κ) LCPs. New search directions and proximity measures are proposed based on a new kernel function which has linear growth term. We showed that if a strictly feasible starting point...

We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set B of at most three bases, each of a different type, in each iteration: a primal feasible basis Bp, a dual feasible basis Bd and a primal-and-dual infeasible basis Bi. From each B ∈ B, it evaluates the primal and dual feasibility of all primal and dual pivots to...

In this technical report the new version of the software Dgc tool is presented. This tool allows us to build up irregular graph pyramids by dual graph contraction. The graph pyramid consists of a stack of levels (pair of graphs), each of which has a primal level and its dual. Every successive level is a reduced version of the level below. Primal level and its dual represent a primal graph and i...

We propose a “cryptographic” interpretation for the propositional connectives of primal infon logic introduced by Y. Gurevich and I. Neeman and prove the corresponding soundness and completeness results. Primal implication φ→p ψ corresponds to the encryption of ψ with a secret key φ, primal disjunction φ ∨p ψ is a group key and ⊥ reflects some backdoor constructions such as full superuser permi...

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov’s excessive gap technique in a structured fashion and unifies it with smoothing and primal-dual...

Given an integer polyhedron PI ⊂ R, an integer point x̄ ∈ PI , and a point x∗ ∈ R \ PI , the primal separation problem is the problem of finding a linear inequality which is valid for PI , violated by x∗, and satisfied at equality by x̄. The primal separation problem plays a key role in the primal approach to integer programming. In this paper we examine the complexity of primal separation for se...

We propose a family of search directions based on primal-dual entropy in the context of interior point methods for linear programming. This new family contains previously proposed search directions in the context of primal-dual entropy. We analyze the new family of search directions by studying their primal-dual affine-scaling and constant-gap centering components. We then design primal-dual in...

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual itera...