Some integer formula-encodings and related algorithms

Two Encodings of DNNF Theories

The paper presents two new compilation schemes of Decomposable Negation Normal Form (DNNF) theories into Conjunctive Normal Form (CNF) and Linear Integer Programming (MIP), respectively. We prove that the encodings have useful properties such as unit propagation on the CNF formula achieves domain consistency on the DNNF theory. The approach is evaluated empirically on random as well as real-wor...

Generating All Partitions: A Comparison Of Two Encodings

Integer partitions may be encoded as either ascending or descending compositions for the purposes of systematic generation. Many algorithms exist to generate all descending compositions, yet none have previously been published to generate all ascending compositions. We develop three new algorithms to generate all ascending compositions and compare these with descending composition generators fr...

Generated the Integer Null Space and Conditions for Determination of an Integer Basis Using the ABS Algorithms

Generalized Totalizer Encoding for Pseudo-Boolean Constraints

Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), ...

3-difference cordial labeling of some cycle related graphs

Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...