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This paper is concerned with the design and analysis of improved algorithms for determining the optimal length resolution refutation (OLRR) of a system of difference constraints over an integral domain. The problem of finding short explanations for unsatisfiable Difference Constraint Systems (DCS) finds applications in a number of design domains including… (More)

Extending linear constraints by admitting parameters allows for more abstract problem modeling and reasoning. A lot of focus has been given to conducting research that demonstrates the usefulness of parameterized linear constraints and implementing tools that utilize their modeling strength. However, there is no approach that considers basic theoretical… (More)

A Quantified Linear Implication (QLI) is an inclusion query over two polyhedral sets, with a quantifier string that specifies which variables are existentially quantified and which are universally quantified. Equivalently, it can be viewed as a quantified implication of two systems of linear inequalities. In this paper, we provide a 2-person game semantics… (More)

The undirected negative cost cycle detection (UNCCD) problem is concerned with checking whether an undirected, weighted graph contains a negative cost cycle. Known approaches for solving this problem involve reducing it to either the minimum weight $$b$$ b -matching problem or the minimum weight $$T$$ T -join problem. In this paper, we formally describe… (More)

In this paper, we discuss a new combinatorial certifying algorithm for the problem of checking linear feasibility in Unit Two Variable Per Inequality (UTVPI) constraints. A UTVPI constraint has at most two non-zero variables and the coefficients of the non-zero variables belong to the set $$\{+1,\ -1\}$$ { + 1 , - 1 } . These constraints occur in a number… (More)

This paper discusses the implementation of a new parallel algorithm for the negative cost girth (NCG) problem. The girth of an unweighted graph (directed or undirected) is defined as the length of the shortest cycle in the graph. We extend the notion of girth to networks with arbitrary weights in the following way: The negative cost girth of a network is… (More)

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