We investigate some attractive features of the 1-D sequence of pixels produced by the peano traversal of an image. We introduce two new hardware operations called bit-spreaded-meshing and its inverse bit-collation to produce and invert the sequence in real-time. A compact binary tree built using this sequence at its base implicitly contains the well known quadtree of the image also. The binary ...

Given an undirected graph G=(V,E), the longest induced path problem (LIPP) consists of obtaining a maximum cardinality subset W⊆V such that W induces simple in G. In this paper, we propose two new formulations with exponential number constraints for problem, together effective branch-and-cut procedures its solution. While first formulation (cec) is based on explicitly eliminate cycles, second o...

When solving Constraint Satisfaction Problems (CSPs), it is desirable to find multiple solutions, or to find solutions that are robust, allowing us to modify the values of variables without breaking the solution. Furthermore, we would like to be able to represent these multiple solutions in a compact manner. We present a method for improving the performance of, and solutions returned by, stocha...

Iterative-improvement 2-way min-cut partitioning is an important phase in most circuit placement tools, and finds use in many other CAD applications. Most iterative improvement techniques for circuit netlists like the FiducciaMattheyses (FM) method compute the gains of nodes using local netlist information that is only concerned with the immediate improvement in the cutset. This can lead to mis...

Consider a set of terminal nodes K that belong to a network whose nodes are connected by links that fail independently with known probabilities. We introduce a method for estimating any performability measure that depends on the hop distance between terminal nodes. It generalises previously introduced Monte Carlo methods for estimation of the K-reliability of networks with variance reduction co...

A fullerene, which is a 3-connected cubic plane graph whose faces are pentagons and hexagons, is cyclically 5 edge-connected. For a fullerene of order n, it is customary to index the eigenvalues in non-increasing order λ1 ≥ λ2 ≥ · · · ≥ λn. It is known that the largest eigenvalue is 3. Let R = {fi | i ∈ Zl} be a set of l faces of a fullerene F such that fi is adjacent to fi+1, i ∈ Zl, via an ed...

Given a directed graph G, a set of k terminals and an integer p, the Directed Vertex Multiway Cut problem asks if there is a set S of at most p (nonterminal) vertices whose removal disconnects each terminal from all other terminals. Directed Edge Multiway Cut is the analogous problem where S is a set of at most p edges. These two problems indeed are known to be equivalent. A natural generalizat...

The cut-set bound developed by Cover and El Gamal in 1979 has since remained the best known upper bound on the capacity of the Gaussian relay channel. We develop a new explicit upper bound on the capacity of the Gaussian primitive relay channel which is tighter than the cut-set bound. Combined with a simple tensorization argument, this result also implies that the current capacity approximation...

Given a graph with weight associated each vertex , the maximum weighted induced forest problem (MWIF) consists of encountering subset vertices such that induces forest. This NP-hard is known to be equivalent minimum feedback set problem, which has applicability in variety domains. The closely related tree (MWIT), on other hand, requires tree. We propose two new integer programming formulations ...