Neeraj Mittal

On slicing a distributed computation

We introduce the notion of a slice of a distributed computation. A slice of a distributed computation with respect to a global predicate is a computation which captures those and only those consistent cuts of the original computation which satisfy the global predicate. We show that a slice exists for a global predicate iff the predicate is a regular predicate. We then give an efficient algorithm for computing the slice and show applications of slicing to testing and debugging of distributed programs.

An Asynchronous Neighbor Discovery Algorithm for Cognitive Radio Networks

Cognitive radio (CR) technology is a promising emerging technology that enables a more efficient usage of already assigned spectrum. However, before CR networks can be deployed, new algorithms and protocols need to be developed. When forming an ad-hoc cognitive radio network (CRN), one of the fundamental tasks is to determine the neighbors of each node and channels that can be used to communicate among neighbors. The nature of the CRN makes this a challenging problem. Specifically in CRN, not only the network is multi-channel, but the channels available at different nodes may be different. Furthermore no time synchronization may be available to nodes. In this paper, we propose an asynchronous distributed algorithm that allows nodes to discover their neighbors and channels that can be used to communicate with them in a single-hop CRN.

Fast concurrent lock-free binary search trees

We present a new lock-free algorithm for concurrent manipulation of a binary search tree in an asynchronous shared memory system that supports search, insert and delete operations. In addition to read and write instructions, our algorithm uses (single-word) compare-and-swap (CAS) and bit-test-and-set (SETB) atomic instructions, both of which are commonly supported by many modern processors including Intel~64 and AMD64. In contrast to existing lock-free algorithms for a binary search tree, our algorithm is based on marking edges rather than nodes. As a result, when compared to other lock-free algorithms, modify (insert and delete) operations in our algorithm work on a smaller portion of the tree, thereby reducing conflicts, and execute fewer atomic instructions (one for insert and three for delete). Our experiments indicate that our lock-free algorithm significantly outperforms all other algorithms for a concurrent binary search tree in many cases, especially when contention is high, by as much as 100%.

Time-efficient distributed layer-2 auto-configuration for cognitive radio networks

Cognitive radios (CR) have the ability to dynamically adapt to local spectrum availability. In a network comprised of CR-enabled devices, layer-2 auto-configuration involves determining a common set of channels to facilitate communication among participating nodes. This is a unique challenge as nodes in the CR network may be unaware of (a) their neighbors and (b) the channels on which they can communicate with a neighbor. In this paper, we propose a time-efficient distributed algorithm for layer-2 auto-configuration for a CR network. Our algorithm finds the globally common channel set in 2MN+O(DN) timeslots, where each node is assigned a unique identifier from the range [1,...,N], M is the maximum number of channels available for communication, and D is the diameter of the network. All nodes know M and N. We present both diameter-aware and diameter-unaware versions of the algorithm. We then show that the proposed algorithms are efficient by proving a matching lower bound. Finally, we investigate a special case when nodes have more knowledge available at their disposal and discuss how the time-complexity of our algorithm can be improved under this case.

Computation Slicing: Techniques and Theory

We generalize the notion of slice introduced in our earlier paper [6]. A slice of a distributed computation with respect to a global predicate is the smallest computation that contains all consistent cuts of the original computation that satisfy the predicate. We prove that slice exists for all global predicates. We also establish that it is, in general, NP-complete to compute the slice. An optimal algorithm to compute slices for special cases of predicates is provided. Further, we present an efficient algorithm to graft two slices, that is, given two slices, either compute the smallest slice that contains all consistent cuts that are common to both slices or compute the smallest slice that contains all consistent cuts that belong to at least one of the slices. We give application of slicing in general and grafting in particular to global property evaluation of distributed programs. Finally, we show that the results pertaining to consistent global checkpoints [14,18] can be derived as special cases of computation slicing.

Minimal time broadcasting in cognitive radio networks

This paper addresses time-efficient broadcast scheduling problem in Cognitive Radio (CR) Networks. Cognitive Radio is a promising technology that enables the use of unused spectrum in an opportunistic manner. Because of the unique characteristics of CR technology, the broadcast scheduling problem in CR networks needs unique solutions. Even for single channel wireless networks, finding a minimum-length broadcast schedule is an NP-hard problem. In addition, the multi-channel nature of the CR networks, especially the non-uniform channel availability, makes it a more complex problem to solve. In this paper, we first present an Integer Linear Programming formulation (ILP) to determine the minimum broadcast schedule length for a CR network. We then present two heuristics to construct minimal length broadcast schedules. Comparison of optimal results (found by solving the ILP formulation) with the result of the heuristics through simulation shows that both heuristics produce schedules of either optimal or very closer to optimal lengths.

On detecting global predicates in distributed computations

Monitoring of global predicates is a fundamental problem in asynchronous distributed systems. This problem arises in various contexts, such as design, testing and debugging, and fault tolerance of distributed programs. In this paper, we establish that the problem of determining whether there exists a consistent cut of a computation that satisfies a predicate in k-CNF (k/spl ges/2), in which no two clauses contain variables from the same process, is NP-complete in general. A polynomial-time algorithm to find the consistent cut, if it exists, that satisfies the predicate for special cases is provided. We also give algorithms (albeit exponential) that can be used to achieve an exponential reduction in time over existing techniques for solving the general version. Furthermore, we present an algorithm to determine whether there exists a consistent cut of a computation for which the sum x/sub 1/+x/sub 2/+/spl middot//spl middot//spl middot/+x/sub n/ exactly equals some constant k, where each x/sub i/ is an integer variable on a process p/sub i/ such that it is incremented or decremented by at most one at each step. As a corollary, any symmetric global predicate on Boolean variables, such as absence of simple majority and exclusive-OR of local predicates, can now be detected. Additionally, the problem is proved to be NP-complete if each x/sub i/ can be changed by an arbitrary amount at each step. Our results solve the previously open problems in predicate detection proposed by V.K. Garg (1997) and bridge the wide gap between the known tractability and intractability results that have existed until now.

Debugging distributed programs using controlled re-execution

Distributed programs are hard to write. A distributed debugger equipped with the mechanism to re-execute the traced computation in a controlled fashion can greatly facilitate the detection and localization of bugs. This approach gives rise to a general problem, called predicate control problem, which takes a computation and a safety property specified on the computation, and outputs a controlled computation that maintains the property. We define a class of global predicates, called region predicates, that can be controlled efficiently in a distributed computation. We prove that the synchronization generated by our algorithm is optimal. Further, we introduce the notion of an admissible sequence of events and prove that it is equivalent to the notion of predicate control. We then give an efficient algorithm for the class of disjunctive predicates based on the notion of an admissible sequence.

On neighbor discovery in cognitive radio networks

A cognitive radio node is a radio device capable of operating over multiple channels. As a result, a network consisting of one or more cognitive radio nodes can adapt to varying channel availability in its geographical region by dynamically changing the channel (or channels) nodes are using for communication. We investigate the problem of designing a fast deterministic algorithm for neighbor discovery in an undirected network consisting of one or more cognitive radio nodes when different nodes may have different subsets of channels available for communication at their location. We say that a neighbor discovery algorithm is fast if its time-complexity is polynomial in actual network-size. We prove that it is impossible to devise a fast algorithm to solve the neighbor discovery problem if nodes are neither size-aware nor collision-aware. When nodes are collision-aware, we present a fast algorithm for neighbor discovery with time-complexity of O(pmlogn), where p denotes the actual number of nodes present in the network, n denotes the size of space used for assigning labels to the nodes, and m denotes the number of channels over which nodes can operate. Our algorithm has the desirable property that every node knows when the neighbor discovery has completed and, moreover, all nodes terminate at the same time. When nodes are size-aware, we use a gossiping algorithm for a single-channel network with large labels that was proposed recently to derive a fast adaptive algorithm for neighbor discovery. We also investigate the neighbor discovery problem when the network may be directed. Finally, we describe a way to speed up neighbor discovery when nodes are collision-aware and channel availability sets of neighboring nodes do not vary significantly.

A Lightweight Solution for Defending Against Deauthentication/Disassociation Attacks on 802.11 Networks

In this paper we investigate a special type of denial of service (DoS) attack on 802.11-based networks, namely deauthentication/disassociation attack. In the current IEEE 802.11 standards, whenever a wireless station wants to leave the network, it sends a deauthentication or disassociation frame to the access point. These two frames, however, are sent unencrypted and are not authenticated by the access point. Therefore, an attacker can launch a DoS attack by spoofing these messages and thus disabling the communication between a wireless device and its access point. We propose an efficient solution based on a one way hard function to verify that a deauthentication/disassociation frame is from a legitimate station. We implement our solution on some 802.11 devices and the experimental results show that our protocol is highly effective against this DoS attack.