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Consider an n-vertex graph G = (V,E) of maximum degree Delta, and suppose that each vertex v \in V hosts a processor. The processors are allowed to communicate only with their neighbors in G. The communication is synchronous, i.e., it…
Graph matching aims to find correspondences between two graphs. It is a fundamental task in pattern recognition. The classical spectral matching algorithm has time complexity $\mathcal{O}(n^4)$ and space complexity $\mathcal{O}(n^4)$, where…
Given a set $P$ of $n$ weighted points and a set $H$ of $n$ half-planes in the plane, the hitting set problem is to compute a subset $P'$ of points from $P$ such that each half-plane contains at least one point from $P'$ and the total…
The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s.…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
We study theoretical runtime guarantees for a class of optimization problems that occur in a wide variety of inference problems. these problems are motivated by the lasso framework and have applications in machine learning and computer…
Important papers have appeared recently on the problem of indexing binary strings for jumbled pattern matching, and further lowering the time bounds in terms of the input size would now be a breakthrough with broad implications. We can…
Beam hopping (BH) is a satellite communications technique in which sets of beams are sequentially illuminated over a defined time interval. Geographically varying the duty cycle of satellite transmission allows for reduced resource wastage…
We study Clustered Planarity with Linear Saturators, which is the problem of augmenting an $n$-vertex planar graph whose vertices are partitioned into independent sets (called clusters) with paths - one for each cluster - that connect all…
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected…
A central problem in parameterized algorithms is to obtain algorithms with running time $f(k)\cdot n^{O(1)}$ such that $f$ is as slow growing function of the parameter $k$ as possible. In particular, a large number of basic parameterized…
We give algorithms with running time $2^{O({\sqrt{k}\log{k}})} \cdot n^{O(1)}$ for the following problems. Given an $n$-vertex unit disk graph $G$ and an integer $k$, decide whether $G$ contains (1) a path on exactly/at least $k$ vertices,…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…
This paper proposes a novel power-efficient light-emitting diode (LED) placement algorithm for indoor visible light communication (VLC). In the considered model, the LEDs can be designedly placed for high power efficiency while satisfying…