Integer linear programming (ILP) problems occur frequently in many applications. In practice, alternative optima are useful since they allow the decision maker to choose from multiple solutions without experiencing any deterioration in the objective function. This study proposes a general integer cut to exclude the previous solution and presents an algorithm to identify all alternative optimal ...

We will analyze mixed-0/1 second-order cone programs where the continuous and binary variables are solely coupled via the conic constraints. We devise a cutting-plane framework based on an implicit Sherali-Adams reformulation. The resulting cuts are very effective as symmetric solutions are automatically cut off and each equivalence class of 0/1 solutions is visited at most once. Further, we pr...

In this essay we analyze properties of the lifted-cut linear programming relaxation of the Steiner Forest problem introduced by Könemann, Leonardi and Schäfer. We introduce this new formulation and prove some basic properties establishing that it is in fact a valid relaxation and analyzing the integrality gap. We are interested in analyzing the possible half-integrality of this relaxation and c...

Partitioning driven placement approaches are often preferred for fast and scalable solutions to large placement problems. However, due to the inaccuracy of representing wirelength objective by cut objective the quality of such placements often trails the quality of placements produced by pure wirelength driven placements. In this paper we present THETO, a new partitioning driven placement algor...

The Two-sided Two-layer Crossing Minimization (TSCM) problem calls for minimizing a quadratic objective function subject to a set of ordering constraints, where all variables are binary. This NP-hard problem has important applications in graph drawing as a key step in drawing hierarchical graphs. In this paper, we propose two new exact algorithms for the TSCM problem. One is an LP-based branch-...

Abstract We study a family of gradient obstacle problems on compact Riemannian manifold. prove that the solutions these free boundary are uniformly semiconcave and, as consequence, we obtain some fine convergence results for and their boundaries. More precisely, show elastic $$\lambda $$ λ -elastic sets Hausd...

Load balancing plays an important role in parallel numerical simulations. State-of-the-art libraries addressing this problem base on vertex exchange heuristics that are embedded in a multilevel scheme. However, these are hard to parallelize due to their sequential nature. Furthermore, libraries like Metis and Jostle focus on a small edge-cut and cannot obey constraints like connectivity and str...

This paper proposes a novel analysis, called cardinality analysis, to approximate the number of solutions to a goal. The analysis is an instantiation of a new abstract interpretation framework for full Prolog (without dynamic predicates) based on sequences of substitutions. The abstract domain captures not only modes and types but also lower and upper bounds on the number of solutions and infor...

The oxidation reaction of piranha solutions with purified HiPco carbon nanotubes was measured as a function of temperature. At high temperatures, piranha is capable of attacking existing damage sites, generating vacancies in the graphene sidewall, and consuming the oxidized vacancies to yield short, cut nanotubes. Increased reaction time results in increasingly shorter nanotubes. However, signi...