# Sambuddha Roy's research while affiliated with Microsoft and other places

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## Publications (40)

We study the problem of maximizing the throughput of jobs wherein each job consists of multiple tasks. Consider a system offering a capacity of one unit. We are given a set of jobs, each consisting of a sequence of r tasks. Each task is associated with a demand and an interval where it should be scheduled. Each job has a profit associated with it....

We consider the question of finding communities in large social networks. In literature and practice, “communities” refer to a well-connected subgraph of the entire network. For instance, the notion of graph density has been considered as a reasonable measure of a community. Researchers have also looked at the minimum degree of a subgraph as a meas...

We consider the problem of scheduling a set of jobs on a system that offers certain resource, wherein the amount of resource offered varies over time. For each job, the input specifies a set of possible scheduling instances, where each instance is given by starting time, ending time, profit and resource requirement. A feasible solution selects a su...

In this paper, we study a class of set cover problems that satisfy a special
property which we call the {\em small neighborhood cover} property. This class
encompasses several well-studied problems including vertex cover, interval
cover, bag interval cover and tree cover. We design unified distributed and
parallel algorithms that can handle any set...

We describe a primal-dual framework for the design and analysis of online
convex optimization algorithms for {\em drifting regret}. Existing literature
shows (nearly) optimal drifting regret bounds only for the $\ell_2$ and the
$\ell_1$-norms. Our work provides a connection between these algorithms and the
Online Mirror Descent ($\omd$) updates; on...

This paper considers the problem of maximizing the throughput of jobs wherein each job consists of multiple tasks. Consider a system offering a uniform capacity of a resource (say unit bandwidth). We are given a set of jobs, each consisting of a sequence of at most r tasks. Each task is associated with a window (specified by a release time and a de...

In this paper we study the unsplittable flow problem (UFP) on tree networks in a distributed setting. We have a set of processors (or agents) and a set of tree networks defined over some vertex set. Each processor can access a subset of the tree networks. Each edge in each of the tree networks is associated with a capacity. Each processor has a dem...

In this paper, we consider the problem of choosing a minimum cost set of
resources for executing a specified set of jobs. Each input job is an interval,
determined by its start-time and end-time. Each resource is also an interval
determined by its start-time and end-time; moreover, every resource has a
capacity and a cost associated with it. We con...

In this paper we consider the problem of finding the {\em densest} subset
subject to {\em co-matroid constraints}. We are given a {\em monotone
supermodular} set function $f$ defined over a universe $U$, and the density of
a subset $S$ is defined to be $f(S)/\crd{S}$. This generalizes the concept of
graph density. Co-matroid constraints are the fol...

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices ‹u, v›, along with a profit; the processor wishes to send data between u and v. Towards that goal, the processor needs to select a gra...

We consider a natural generalization of the Partial Vertex Cover problem.
Here an instance consists of a graph G = (V,E), a positive cost function c: V->
Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$
for each partition $P_i$. The goal is to find a minimum cost set of vertices
which cover at least $k_i$ edges from the...

We consider the problem of scheduling jobs that require multiple resources such as memory, bandwidth and processors. For each job, the input specifies start time, finish time and profit; the input also specifies the job's requirement for each resource. Each resource has a fixed capacity (called bandwidth). A feasible solution is a subset of jobs su...

We consider the problem of allocating resources to satisfy demand requirements varying over time. The input specifies a demand for each timeslot. Each resource is specified by a start-time, end-time, an associated cost and a capacity. A feasible solution is a multiset of resources such that at any point of time, the sum of the capacities offered by...

We consider the problem of allocating resources for completing a collection of jobs. Each resource is specified by a start-time, finish-time and the capacity of resource available and has an associated cost, and each job is specified by a start-time, finish-time and the amount of the resource required (demand) during this interval. A feasible solut...

Consider the following problem which often arises in contact center scheduling scenarios. We are given a set of employees where each employee can be deployed for shifts consisting of L consecutive time units. Further, each employee specifies a set of possible start times, and can be deployed for a bounded number of shifts only. At each point of tim...

We consider the problem of constructing decision trees for entity identification from a given relational table. The input is a table containing information about a set of entities over a fixed set of attributes and a probability distribution over the set of entities that specifies the likelihood of the occurrence of each entity. The goal is to cons...

We consider the problem of constructing decision trees for entity identification from a given relational table. The in- put is a table containing information about a set of enti- ties over a fixed set of attributes and a probability distri- bution over the set of entities that specifies the likelihood of the occurrence of each entity. The goal is t...

We continue an investigation into resource-bounded Kolmogorov complexity [ABK + 06], which highlights the close connections between circuit complexity and Levin’s time-bounded Kolmogorov complexity measure Kt (and other measures with a similar flavor), and also exploits derandomization techniques to provide new insights regarding Kolmogorov complex...

We consider the problem of scheduling a set of resources over time. Each resource is specified by a set of time intervals
(and the associated amount of resource available), and we can choose to schedule it in one of these intervals. The goal is
to maximize the number of demands satisfied, where each demand is an interval with a starting and ending...

The maximum independent set problem MaxIS on general graphs is known to be NP-hard to approximate within a factor of n 1-ϵ , for any ϵ>0. However, there are many “easy” classes of graphs on which the problem can be solved in polynomial time. In this context, an interesting question is that of computing the maximum independent set in a graph that ca...

. We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity
of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2k, for constant k. On the other hand, we show that for any other modulus and in th...

We study the complexity of restricted versions ofs-t-connectivity, which is the standard complete problem forNL. In particular, we focus on different classes ofplanar graphs, of which grid graphs are an important special case. Our main results are: • Reachability in graphs of genus one is logspace-equivalent to reachability in grid graphs (and in p...

We consider the problem of constructing decision trees for entity identification from a given table. The input is a table
containing information about a set of entities over a fixed set of attributes. The goal is to construct a decision tree that
identifies each entity unambiguously by testing the attribute values such that the average number of te...

We present a 2-approximation algorithm for the problem of finding the maximum weight K-colorable subgraph in a given chordal graph with node weights. The running time of the al- gorithm is O(K(n+m)), where n and m are the number of vertices and edges in the given graph.

We continue an investigation into resource-bounded Kolmogorov complexity (Allender et al., 2006 [4]), which highlights the close connections between circuit complexity and Levin's time-bounded Kolmogorov complexity measure Kt (and other measures with a similar flavor), and also exploits derandomization techniques to provide new insights regarding K...

We study some problems solvable in deterministic polynomial time given oracle access to the promise version of the Arthur-Merlin class AM. The main result is that \({{\rm BPP}^{\rm NP}_{||}} \subseteq {{\rm P}^{{{\rm pr}{\rm AM}}}_{||}}\). An important property of the class \({{\rm P}^{{{\rm pr}{\rm AM}}}_{||}}\) is that it can be derandomized as \...

We present a deterministic Logspace procedure, which, given a bipartite planar graph on n vertices, assigns O(log n) bits long weights to its edges so that the minimum weight perfect matching in the graph becomes unique. The Isolation Lemma as described in Mulmuley et al. (Combinatorica 7(1):105–131, 1987) achieves the same for general graphs using...

Social networks refer to structures made of nodes that represent people or other entities embedded in a social context, and whose edges represent interaction between entities. Typical examples of social networks are collaboration networks in a research community, networks arising out of interaction between colleagues of large organization etc. Soci...

We show that Sp 2 P prAM , where Sp2 is the symmetric alternation class and prAM refers to the promise version of the Arthur-Merlin class AM. This is derived as a consequence of our main result that presents an FPprAM algorithm for nding a small set of \collectively irrefutable certicates" of a given S 2-type matrix. The main result also yields som...

We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2^k, for constant k. On the other hand, we show that for any other modulus and in the...

We introduce a new class \(\rm {O}^p_2\) as a subclass of the symmetric alternation class \(\rm {S}^p_2\). An \(\rm {O}^p_2\) proof system has the flavor of an \(\rm {S}^p_2\) proof system, but it is more restrictive in nature. In an \(\rm {S}^p_2\) proof system, we have two competing provers and a verifier such that for any input, the honest prove...

We study the complexity of restricted versions ofst- connectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since reachability on grid graphs is logspace-equivalent to reachability in general planar digraphs, and reachability on certain classes of grid graphs gives natural examples of problems tha...

We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the planar case.
We also consider a previously-studied subclass...

We show that ACC<sup>0</sup> is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC<sup>0</sup>. Thus polylogarithmic genus provides no additional computational power in this model....

We continue an investigation of resource-bounded Kolmogorov complexity and derandomization techniques begun in [E. Allender (2001), E. Allender et al., (2002)]. We introduce nondeterministic time-bounded Kolmogorov complexity measures (KNt and KNT) and examine the properties of these measures using constructions of hitting set generators for nondet...

We continue an investigation of resource-bounded Kolmogorov complexity and derandomization techniques begun in [2, 3]. We introduce nondeterministic time-bounded Kolmogorov complexity measures (KNt and KNT) and examine the properties of these measures using constructions of hitting set generators for nondeterministic circuits [22, 26]. We observe t...

We extend the lower bound techniques of [14], to the unbounded-error probabilistic model. A key step in the argument is a generalization of Nepomnjasci's theorem from the Boolean setting to the arithmetic setting. This generalization is made possible, due to the recent discovery of logspace-uniform TC 0 circuits for iterated multiplication [9].

## Citations

... The traditional resource allocation techniques can be categorized into approximation-based, heuristic-based, metaheuristic-based, and game-theoretic-based. Approximation methods find a quasi-optimal solution (within polynomial time [94]) to NP-hard problems that are guaranteed to be close to the optimal solution [95]. In the context of resource allocation, the methods for designing approximation algorithms include greedy-based [96], [97], [98], local search-based [99], [100], primal-dual-based [101], [102], and LP-rounding-based [103], [104], [105]. ...

... Venkatesan et al. [23] study the problem of maximizing the throughput of jobs where each job consists of multiple tasks. Different from the SplitJob problem, each task has a window where the task can be scheduled any time within the window subject to the processing length. ...

... The BagUFP problem has also been studied under distributed models, and constant factor approximation algorithms are known in the uniform capacity setting, and logarithmic factor approximations in the non-uniform capacity setting (Panconesi and Sozio 2010;Chakaravarthy et al. 2012Chakaravarthy et al. , 2013. These algorithms are based on the primal-dual paradigm and they also apply to the parallel setting. ...

... Moreover, the online game in MTS differs from the online learning setup in that it follows the 1lookahead setting where the player has access to the reward function f t before estimating x t . The typical instantiation of the movement cost in MTS is a total variation penalty T −1 t=1 x t − x t+1 2 , that can also be defined with non-Euclidean norms (Bera et al., 2013). While the movement cost introduces dependencies across actions x t in successive rounds, we note that, to the best of our knowledge, previous work only considered movement costs with an additive structure. ...

... This in turn implies that prAM ⊆ P NP . A close inspection of our proof, and the proofs in [8] that it relies on, reveals that for obtaining an exponential-size lower bound, it is enough to derandomize the lower bound protocol of Goldwasser- Sipser [12] (and not necessarily the whole of prAM), which is an Arthur-Merlin protocol for proving that a set which can be recognized by a small circuit is large (see Lemma 3.3 for the exact formulation of this problem). ...

... If the input is a DNF instead of a truth-table then we know of the following result: s 1 4 −ǫ factor approximation of the minimum DNF size of an input DNF of size s is not in P, for every ǫ ∈ (0, 1), assuming Σ p 2 DTIME(n O(log n) ) [Uma99]. 33 An integer of the form pq for primes p and q, where p = q = 3 mod 4. 34 Similar results have also been shown for NC 1 and TC 0 circuits [AKRR03]. 35 A deterministic analogue of this result was shown in [Vol16]. 36 This property is satisfied with high probability if the coefficients of the input polynomial are perturbed slightly by a random noise. ...

... These results have appeared in [16]. ...

... They extend the greedy method of [17] and show that it achieves a 3-approximation guarantee for some special cases of this problem. [8] recently improved the approximation guarantee of the greedy algorithm of [12] for problem (3) to a factor 2. The time complexity of this greedy algorithm is O(kn 3 ), where n is the number of experts and k := m j=1 kj is the minimum number of experts required. ...

... Whether we can derandomize the isolation lemma is the next natural question to ask. The question has been answered positively for matching in some special graph classes [21,8,9]. However, it remains open even for matching in bipartite graphs. ...

... The BagUFP problem has also been studied under distributed models, and constant factor approximation algorithms are known in the uniform capacity setting, and logarithmic factor approximations in the non-uniform capacity setting (Panconesi and Sozio 2010;Chakaravarthy et al. 2012Chakaravarthy et al. , 2013. These algorithms are based on the primal-dual paradigm and they also apply to the parallel setting. ...