Srinivasan Parthasarathy

Minimizing broadcast latency and redundancy in ad hoc networks

Network wide broadcasting is a fundamental operation in ad hoc networks. In broadcasting, a source node sends a message to all the other nodes in the network. In this paper, we consider the problem of collision-free broadcasting in ad hoc networks. Our objective is to minimize the latency and the number of transmissions in the broadcast. We show that minimum latency broadcasting is NP-complete for ad hoc networks. We also present a simple distributed collision-free broadcasting algorithm for broadcasting a message. For networks with bounded node transmission ranges, our algorithm simultaneously guarantees that the latency and the number of transmissions are within O(1) times their re spective optimal values. Our algorithm and analysis extend to the case when multiple messages are broadcast from multiple sources. Experimental studies indicate that our algorithms perform much better in practice than the analytical guarantees provided for the worst case.

Dependent rounding and its applications to approximation algorithms

We develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include:---low congestion multi-path routing;---richer random-graph models for graphs with a given degree-sequence;---improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and---fair scheduling of jobs on unrelated parallel machines.

Approximation Algorithms for Computing Capacity of Wireless Networks with SINR Constraints

A fundamental problem in wireless networks is to estimate its throughput capacity - given a set of wireless nodes, and a set of connections, what is the maximum rate at which data can be sent on these connections. Most of the research in this direction has focused on either random distributions of points, or has assumed simple graph-based models for wireless interference. In this paper, we study capacity estimation problem using the more general Signal to Interference Plus Noise Ratio (SINR) model for interference, on arbitrary wireless networks. The problem becomes much harder in this setting, because of the non-locality of the SINR model. Recent work by Moscibroda et al. (2006) has shown that the throughput in this model can differ from graph based models significantly. We develop polynomial time algorithms to provably approximate the total throughput in this setting.

Cross-layer latency minimization in wireless networks with SINR constraints

Recently, there has been substantial interest in the design of cross-layer protocols for wireless networks. These protocols optimize certain performance metric(s) of interest (e.g. latency, energy, rate) by jointly optimizing the performance of multiple layers of the protocol stack. Algorithm designers often use geometric-graph-theoretic models for radio interference to design such cross-layer protocols. In this paper we study the problem of designing cross-layer protocols for multi-hop wireless networks using a more realistic Signal to Interference plus Noise Ratio (SINR) model for radio interference. The following cross-layer latency minimization problem is studied: Given a set V of transceivers, and a set of source-destination pairs, (i) choose power levels for all the transceivers, (ii) choose routes for all connections, and (iii) construct an end-to-end schedule such that the SINR constraints are satisfied at each time step so as to minimize the make-span of the schedule (the time by which all packets have reached their respective destinations). We present a polynomial-time algorithm with provable worst-case performance guarantee for this cross-layer latency minimization problem. As corollaries of the algorithmic technique we show that a number of variants of the cross-layer latency minimization problem can also be approximated efficiently in polynomial time. Our work extends the results of Kumar et al. (Proc. SODA, 2004) and Moscibroda et al. (Proc. MOBIHOC, 2006). Although our algorithm considers multiple layers of the protocol stack, it can naturally be viewed as compositions of tasks specific to each layer --- this allows us to improve the overall performance while preserving the modularity of the layered structure.

Dependent rounding in bipartite graphs

We combine the pipage rounding technique of Ageev & Sviridenko with a recent rounding method developed by Srinivasan (2001), to develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to the following applications: richer random-graph models for graphs with a given degree-sequence; improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, and (iii) capacitated vertex cover; fair scheduling of jobs on unrelated parallel machines. A useful feature of our method is that it lets us prove certain (probabilistic) per-user fairness properties.

Distributed algorithms for coloring and domination in wireless ad hoc networks

We present fast distributed algorithms for coloring and (connected) dominating set construction in wireless ad hoc networks. We present our algorithms in the context of Unit Disk Graphs which are known to realistically model wireless networks. Our distributed algorithms take into account the loss of messages due to contention from simultaneous interfering transmissions in the wireless medium. We present randomized distributed algorithms for (conflict-free) Distance-2 coloring, dominating set construction, and connected dominating set construction in Unit Disk Graphs. The coloring algorithm has a time complexity of O(Δ log2n) and is guaranteed to use at most O(1) times the number of colors required by the optimal algorithm. We present two distributed algorithms for constructing the (connected) dominating set; the former runs in time O(Δ log 2n) and the latter runs in time O(log 2n). The two algorithms differ in the amount of local topology information available to the network nodes. Our algorithms are geared at constructing Well Connected Dominating Sets (WCDS) which have certain powerful and useful structural properties such as low size, low stretch and low degree. In this work, we also explore the rich connections between WCDS and routing in ad hoc networks. Specifically, we combine the properties of WCDS with other ideas to obtain the following interesting applications: An online distributed algorithm for collision-free, low latency, low redundancy and high throughput broadcasting. Distributed capacity preserving backbones for unicast routing and scheduling.

Similarity Searching in Peer-to-Peer Databases

We consider the problem of handling similarity queries in peer-to-peer databases. We propose an indexing and searching mechanism which, given a query object, returns the set of objects in the database that are semantically related to the query. We propose an indexing scheme which clusters data such that semantically related objects are partitioned into a small set of clusters, allowing for a simple and efficient similarity search strategy. Our indexing scheme also decouples object and node locations. Our adaptive replication and randomized lookup schemes exploit this feature and ensure that the number of copies of an object is proportional to its popularity and all replicas are equally likely to serve a given query, thus achieving perfect load balancing. The techniques developed in this work are oblivious to the underlying DHT topology and can be implemented on a variety of structured overlays such as CAN, CHORD, Pastry, and Tapestry. We also present DHT-independent analytical guarantees for the performance of our algorithms in terms of search accuracy, cost, and load-balance; the experimental results from our simulations confirm the insights derived from these analytical models

A unified approach to scheduling on unrelated parallel machines

We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming-, quadratic programming-, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. This algorithm leads to the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan simultaneously exhibit the current-best individual approximations for these criteria; (ii) better-than-two approximation guarantees for scheduling to minimize the Lp norm of the vector of machine-loads, for all 1 < p < ∞; and (iii) the first constant-factor multicriteria approximation algorithms that can handle the weighted completion-time and any given collection of integer Lp norms. Our algorithm has a natural interpretation as a melding of linear-algebraic and probabilistic approaches. Via this view, it yields a common generalization of rounding theorems due to Karp et al. [1987] and Shmoys & Tardos [1993], and leads to improved approximation algorithms for the problem of scheduling with resource-dependent processing times introduced by Grigoriev et al. [2007].

Capacity of Asynchronous Random-Access Scheduling in Wireless Networks

We study the throughput capacity of wireless networks which employ (asynchronous) random-access scheduling as opposed to deterministic scheduling. The central question we answer is: how should we set the channel-access probability for each link in the network so that the network operates close to its optimal throughput capacity? We design simple and distributed channel-access strategies for random-access networks which are provably competitive with respect to the optimal scheduling strategy, which is deterministic, centralized, and computationally infeasible. We show that the competitiveness of our strategies are nearly the best achievable via random-access scheduling, thus establishing fundamental limits on the performance of random- access. A notable outcome of our work is that random access compares well with deterministic scheduling when link transmission durations differ by small factors, and much worse otherwise. The distinguishing aspects of our work include modeling and rigorous analysis of asynchronous communication, asymmetry in link transmission durations, and hidden terminals under arbitrary link-conflict based wireless interference models.

Distributed algorithms for connected domination in wireless networks

We present fast distributed local control connected dominating set (CDS) algorithms for wireless ad hoc networks. We present two randomized distributed algorithms, CDSColor and CDSTop which take into account the effect of wireless interference and the consequent loss of messages during the execution of the algorithm. These algorithms produce a CDS of constant size and constant stretch ratio with high probability, and converge in polylogarithmic running time. Specifically, algorithm CDSColor requires the nodes to know (estimates of) the maximum degree @D and the size of the network n and converges in O(@Dlog^2n) time. Algorithm CDSTop requires the nodes to know their three-hop topology and (an estimate of) the network size n and converges in O(log^2n) time. To the best of our knowledge, these are the first distributed interference-aware CDS algorithms for wireless ad hoc networks which break the linear running-time barrier.