In this paper, we study a combinatorial problem encountered in monetary systems. The problem concerned is to find an optimal solution R(k, n) of a combinatorial problem for some positive integers k and n. To the authors’ knowledge, there is no efficient solutions for this problem in the literatures so far. We first show how to find an efficient recursive construction algorithm based on the back...

By means of an exhaustive computer search we have proved that the strongly regular graphs with parameters (v, k, λ, μ) = (105, 32, 4, 12), (120, 42, 8, 18) and (176, 70, 18, 34) are unique upto isomorphism. Each of these graphs occurs as an induced subgraph in the strongly regular McLaughlin graph. We have used an orderly backtracking algorithm with look-ahead and look-back strategies, applying...

We introduce our work on the backdoor key, a concept that shows promise for characterizing problem hardness in backtracking search algorithms. The general notion of backdoors was recently introduced to explain the source of heavy-tailed behaviors in backtracking algorithms (Williams, Gomes, & Selman 2003a; 2003b). We describe empirical studies that show that the key faction,i.e., the ratio of t...

Many planning and design problems can be characterized as optimal search over a constrained network of conditional choices with preferences. To draw upon the advanced methods of constraint satisfaction to solve these types of problems, many dynamic and flexible CSP variants have been proposed. One such variant is the Weighted Conditional CSP (WCCSP). So far, however, little work has been done t...

Ordering heuristics are a powerful tool in CSP search algorithms. Among the most successful ordering heuristics are heuristics which enforce a fail first strategy by using the min-domain property [HE80, BR96, SG98, Dec 03]. Ordering heuristics have been introduced recently to Asynchronous backtracking (ABT), for distributed constraints satisfaction (DisCSP) [ZM05]. However, the pioneering study...

Logic programming provides a declarative framework for modeling and solving many combinatorial problems. Until recently, it was not competitive with state of the art planning techniques partly due to search capabilities limited to backtracking. Recent development brought more advanced search techniques to logic programming such as tabling that simplifies implementation and exploitation of more ...

The paper presents an iterative forward search framework for solving constraint satisfaction and optimization problems. This framework combines ideas of local search, namely improving a solution by local steps, with principles of depth-first search, in particular extending a partial feasible assignment towards a solution. Within this framework, we also propose and study a conflict-based statist...

In this paper, we introduce δǫα∗ – a minimal coverage, real-time robotic search algorithm that yields a moderately aggressive search path with minimal backtracking. Search performance is bounded by a placing a combinatorial bound, ǫ and δ, on the maximum deviation from the theoretical shortest path and the probability at which further deviations can occur. Additionally, we formally define the n...

An equitable k-coloring of an undirected graph G = (V,E) is a partition of its vertices into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one. As a variant of the graph coloring problem (GCP), the equitable coloring problem (ECP) concerns finding a minimum k for which an equitable k-coloring exists. In this work, we propose a backtrackin...

We analyze two algorithms for solving constraint satisfaction problems. One of these algorithms, Probe Order Backtracking, has an average running time much faster than any previously analyzed algorithm for problems where solutions are common. Probe Order Backtracking uses a probing assignment (a prese-lected test assignment to unset variables) to help guide the search for a solution to a constr...