A potential reduction approach to the frequency assignment problem

AbstractThe frequency assignment problem is the problem of assigning frequencies to transmission links such that either no interference occurs, or the amount of interference is minimized. We present an approximation algorithm for this problem that is inspired by Karmarkar's interior point potential reduction approach to combinatorial optimization problems. A non convex quadratic model of the problem is developed, that is very compact as all interference constraints are incorporated in the objective function. Moreover, optimizing this model may result in finding multiple solutions to the problem simultaneouly. Several preprocessing techniques are discussed. We report on computational experience with both real-life and randomly generated instances

Multi-Channel Scheduling for Fast Convergecast in Wireless Sensor Networks

We explore the following fundamental question - how fast can information be collected from a wireless sensor network? We consider a number of design parameters such as, power control, time and frequency scheduling, and routing. There are essentially two factors that hinder efficient data collection - interference and the half-duplex single-transceiver radios. We show that while power control helps in reducing the number of transmission slots to complete a convergecast under a single frequency channel, scheduling transmissions on different frequency channels is more efficient in mitigating the effects of interference (empirically, 6 channels suffice for most 100-node networks). With these observations, we define a receiver-based channel assignment problem, and prove it to be NP-complete on general graphs. We then introduce a greedy channel assignment algorithm that efficiently eliminates interference, and compare its performance with other existing schemes via simulations. Once the interference is completely eliminated, we show that with half-duplex single-transceiver radios the achievable schedule length is lower-bounded by max(2nk − 1,N), where nk is the maximum number of nodes on any subtree and N is the number of nodes in the network. We modify an existing distributed time slot assignment algorithm to achieve this bound when a suitable balanced routing scheme is employed. Through extensive simulations, we demonstrate that convergecast can be completed within up to 50% less time slots, in 100-node networks, using multiple channels as compared to that with single-channel communication. Finally, we also demonstrate further improvements that are possible when the sink is equipped with multiple transceivers or when there are multiple sinks to collect data

A Review of Interference Reduction in Wireless Networks Using Graph Coloring Methods

The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being focused upon as a problem in today's world. In this paper we analyze the interference reduction problem from a graph theoretical viewpoint. A graph coloring methods are exploited to model the interference reduction problem. However, additional constraints to graph coloring scenarios that account for various networking conditions result in additional complexity to standard graph coloring. This paper reviews a variety of algorithmic solutions for specific network topologies.Comment: 10 pages, 5 figure

Cause Clue Clauses: Error Localization using Maximum Satisfiability

Much effort is spent everyday by programmers in trying to reduce long, failing execution traces to the cause of the error. We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem (MAX-SAT), which asks what is the maximum number of clauses of a Boolean formula that can be simultaneously satisfied by an assignment. At an intuitive level, our algorithm takes as input a program and a failing test, and comprises the following three steps. First, using symbolic execution, we encode a trace of a program as a Boolean trace formula which is satisfiable iff the trace is feasible. Second, for a failing program execution (e.g., one that violates an assertion or a post-condition), we construct an unsatisfiable formula by taking the trace formula and additionally asserting that the input is the failing test and that the assertion condition does hold at the end. Third, using MAX-SAT, we find a maximal set of clauses in this formula that can be satisfied together, and output the complement set as a potential cause of the error. We have implemented our algorithm in a tool called bug-assist for C programs. We demonstrate the surprising effectiveness of the tool on a set of benchmark examples with injected faults, and show that in most cases, bug-assist can quickly and precisely isolate the exact few lines of code whose change eliminates the error. We also demonstrate how our algorithm can be modified to automatically suggest fixes for common classes of errors such as off-by-one.Comment: The pre-alpha version of the tool can be downloaded from http://bugassist.mpi-sws.or