Energy consumption has been increasing over the past half century. Even though ultra-low power consuming appliances are being developed, the amount of energy consumption in homes is increasing because of various appliances being produced for ubiquitous smart home. We propose an adaptive home/building energy management system (A-HEMS/BEMS) for controlling energy consumption using the convergence of heterogeneous sensor/actuator networks. The system goes far beyond traditional auto meter reading (AMR) systems that offer only limited meter-reading functionality and provides a smart infrastructure management that brings new features and benefits to every aspect of our utilities.

We establish several approximate max-integral-flow / min-multicut theorems. While in general this ratio can be very large, we prove strong approximation ratios in the case where the min-multicut is a constant fraction ε of the total capacity of the graph. This setting is motivated by several combinatorial and algorithmic applications. Prior to this work, a general max-integral-flow / min-multicut bound was known only for the special case where the graph is a tree. We prove that, for arbitrary graphs, the max-integral-flow / min-multicut ratio is O(ε-1 log k), where k is the number of commodites; for graphs excluding a fixed subgraph as a minor (for instance, planar graphs), O(1 / ε); and, for dense graphs, O(1√ε). Our proofs are constructive in the sense that we give efficient algorithms which compute either an integral flow achieving the claimed approximation ratios, or a witness that the precondition is violated.

We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough /spl epsiv/, every tester for 3-colorability must have query complexity /spl Omega/(n). This is the first linear lower bound for testing a natural graph property in the bounded-degree model. An /spl Omega/(/spl radic/n) lower bound was previously known. For one-sided error testers, we also show an /spl Omega/(n) lower bound for testers that distinguish 3-colorable graphs from graphs that are (1/3 - /spl alpha/)-far from 3-colorable, for arbitrarily small /spl alpha/. In contrast, a polynomial time algorithm by Frieze and Jerrum (1997) distinguishes 3-colorable graphs from graphs that are 1/5-far from 3-colorable. As a by-product of our techniques, we obtain tight unconditional lower bounds on the approximation ratios achievable by sublinear time algorithms for Max E3SAT, Max E3LIN-2 and other problems.