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Khaled Elbassioni

Publications and source records attributed to Khaled Elbassioni.

At least 37 records · Page 2Linked to original sources
arXiv2021

Access Management in Joint Sensing and Communication Systems: Efficiency versus Fairness

In this paper, we consider a distributed joint sensing and communication (DJSC) system in which multiple radar sensors are deployed. Each sensor is equipped with a sensing function and a communication function, and thus it is a JSC node. The JSC nodes are able to perform sensing their surrounding environments, e.g., weather conditions or available spectrum. Furthermore, they can cooperatively detect and track a common target. The information, i.e., of the environment and target, collected by the JSC nodes is transmitted to a base station (BS) for further processing. As such, different aspects of the target to be viewed simultaneously, which significantly improves the performance of the target detection and tracking. However, both the sensing function and communication function require a certain amount of bandwidth for their operations, and deploying multiple JSC nodes may consume a large amount of bandwidth. Therefore, we investigate the bandwidth allocation problem for the DJSC system. In particular, we aim to optimize the bandwidth allocation to the sensing function and the communication function of the JSC nodes. To improve the allocation efficiency while benefiting the spatial diversity advantage of the DJSC systems, the objective is to maximize the sum of sensing performances, i.e., estimation rates, communication performances, i.e., communication data rates, and fairnesses of all the users. The optimization problem is non-convex and difficult to be solved. For this, we propose a fully polynomial time approximation algorithm, and we prove that the approximation algorithm can guarantee a near-optimal solution with an accuracy bound of $ε$. Furthermore, we propose to use a heuristic algorithm with lower complexity. The simulation results show that both the proposed algorithms are able to achieve the solutions close to the optimum in a computationally efficient fashion.

cs.NI↗
arXiv2021

Online Algorithm for Demand Response with Inelastic Demands and Apparent Power Constraint

A classical problem in power systems is to allocate in-coming (elastic or inelastic) demands without violating the operating constraints of electric networks in an online fashion. Although online decision problems have been well-studied in the literature, a unique challenge arising in power systems is the presence of non-linear constraints, a departure from the traditional settings. A particular example is the capacity constraint of apparent power, which gives rise to a quadratic constraint, rather than typical linear constraints. In this paper, we present a competitive randomized online algorithm for deciding whether a sequence of inelastic demands can be allocated for the requested intervals, subject to the total satisfiable apparent power within a time-varying capacity constraint. We also consider an alternative setting with nodal voltage constraint, using a variant of the online algorithm. Finally, simulation studies are provided to evaluate the algorithms empirically.

cs.DS↗
arXiv2021

Anti Tai Mapping for Unordered Labeled Trees

The well-studied Tai mapping between two rooted labeled trees $T_1(V_1, E_1)$ and $T_2(V_2, E_2)$ defines a one-to-one mapping between nodes in $T_1$ and $T_2$ that preserves ancestor relationship. For unordered trees the problem of finding a maximum-weight Tai mapping is known to be NP-complete. In this work, we define an anti Tai mapping $M\subseteq V_1\times V_2$ as a binary relation between two unordered labeled trees such that any two $(x,y), (x', y')\in M$ violate ancestor relationship and thus cannot be part of the same Tai mapping, i.e. $(x\le x' \iff y\not \le y') \vee (x'\le x \iff y'\not \le y)$, given an ancestor order $x<x'$ meaning that $x$ is an ancestor of $x'$. Finding a maximum-weight anti Tai mapping arises in the cutting plane method for solving the maximum-weight Tai mapping problem via integer programming. We give an efficient polynomial-time algorithm for finding a maximum-weight anti Tai mapping for the case when one of the two trees is a path and further show how to extend this result in order to provide a polynomially computable lower bound on the optimal anti Tai mapping for two unordered labeled trees. The latter result stems from the special class of anti Tai mapping defined by the more restricted condition $x\sim x' \iff y\not\sim y'$, where $\sim$ denotes that two nodes belong to the same root-to-leaf path. For this class, we give an efficient algorithm that solves the problem directly on two unordered trees in $O(|V_1|^2|V_2|^2)$.

cs.DS↗
arXiv2021

Threshold Rounding for the Standard LP Relaxation of some Geometric Stabbing Problems

In the rectangle stabbing problem, we are given a set $\cR$ of axis-aligned rectangles in $\RR^2$, and the objective is to find a minimum-cardinality set of horizontal and/or vertical lines such that each rectangle is intersected by one of these lines. The standard LP relaxation for this problem is known to have an integrality gap of 2, while a better intergality gap of 1.58.. is known for the special case when $\cR$ is a set of horizontal segments. In this paper, we consider two more special cases: when $\cR$ is a set of horizontal and vertical segments, and when $\cR$ is a set of unit squares. We show that the integrality gap of the standard LP relaxation in both cases is stricly less than $2$. Our rounding technique is based on a generalization of the {\it threshold rounding} idea used by Kovaleva and Spieksma (SIAM J. Disc. Math 2006), which may prove useful for rounding the LP relaxations of other geometric covering problems.

cs.CG↗
arXiv2020

Generating clause sequences of a CNF formula

Given a CNF formula $Φ$ with clauses $C_1,\ldots,C_m$ and variables $V=\{x_1,\ldots,x_n\}$, a truth assignment $a:V\rightarrow\{0,1\}$ of $Φ$ leads to a clause sequence $σ_Φ(a)=(C_1(a),\ldots,C_m(a))\in\{0,1\}^m$ where $C_i(a) = 1$ if clause $C_i$ evaluates to $1$ under assignment $a$, otherwise $C_i(a) = 0$. The set of all possible clause sequences carries a lot of information on the formula, e.g. SAT, MAX-SAT and MIN-SAT can be encoded in terms of finding a clause sequence with extremal properties. We consider a problem posed at Dagstuhl Seminar 19211 "Enumeration in Data Management" (2019) about the generation of all possible clause sequences of a given CNF with bounded dimension. We prove that the problem can be solved in incremental polynomial time. We further give an algorithm with polynomial delay for the class of tractable CNF formulas. We also consider the generation of maximal and minimal clause sequences, and show that generating maximal clause sequences is NP-hard, while minimal clause sequences can be generated with polynomial delay.

cs.DM↗
arXiv2020

Computational Aspects of Optimal Strategic Network Diffusion

Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents and treats diffusion as a strategic problem. Here we study the computational aspects of strategic diffusion, i.e., finding the optimal sequence of nodes to activate a network in the minimum time. We prove that finding an optimal solution to this problem is NP-complete in a general case. To overcome this computational difficulty, we present an algorithm to compute an optimal solution based on a dynamic programming technique. We also show that the problem is fixed parameter-tractable when parametrized by the product of the treewidth and maximum degree. We analyze the possibility of developing an efficient approximation algorithm and show that two heuristic algorithms proposed so far cannot have better than a logarithmic approximation guarantee. Finally, we prove that the problem does not admit better than a logarithmic approximation, unless P=NP.

cs.CC↗
arXiv2019

Quasi-polynomial Algorithms for List-coloring of Nearly Intersecting Hypergraphs

A hypergraph $\mathcal{H}$ on $n$ vertices and $m$ edges is said to be {\it nearly-intersecting} if every edge of $\mathcal{H}$ intersects all but at most polylogarthmically many (in $m$ and $n$) other edges. Given lists of colors $\mathcal{L}(v)$, for each vertex $v\in V$, $\mathcal{H}$ is said to be $\mathcal{L}$-(list) colorable, if each vertex can be assigned a color from its list such that no edge in $\mathcal{H}$ is monochromatic. We show that list-colorability for any nearly intersecting hypergraph, and lists drawn from a set of constant size, can be checked in quasi-polynomial time in $m$ and $n$.

cs.DS↗
arXiv2019

Finding Sparse Solutions for Packing and Covering Semidefinite Programs

Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular structure of this class of problems, to obtain more efficient algorithms than those offered by general SDP solvers. For certain applications, such as those described in this paper, it may be desirable to obtain {\it sparse} dual solutions, i.e., those with support size (almost) independent of the number of primal constraints. In this paper, we give an algorithm that finds such solutions, which is an extension of a {\it logarithmic-potential} based algorithm of Grigoriadis, Khachiyan, Porkolab and Villavicencio (SIAM Journal of Optimization 41 (2001)) for packing/covering linear programs.

cs.DS↗
arXiv2019

Price of Anarchy in Algorithmic Matching of Romantic Partners

Algorithmic-matching sites offer users access to an unprecedented number of potential mates. However, they also pose a principal-agent problem with a potential moral hazard. The agent's interest is to maximize usage of the Web site, while the principal's interest is to find the best possible romantic partners. This creates a conflict of interest: optimally matching users would lead to stable couples and fewer singles using the site, which is detrimental for the online dating industry. Here, we borrow the notion of Price-of-Anarchy from game theory to quantify the decrease in social efficiency of online dating sites caused by the agent's self-interest. We derive theoretical bounds on the price-of-anarchy, showing it can be bounded by a constant that does not depend on the number of users of the dating site. This suggests that as online dating sites grow, their potential benefits scale up without sacrificing social efficiency. Further, we performed experiments involving human subjects in a matching market, and compared the social welfare achieved by an optimal matching service against a self-interest matching algorithm. We show that by introducing competition among dating sites, the selfish behavior of agents aligns with its users, and social efficiency increases.

cs.GT↗
arXiv2018

Complex-demand Scheduling Problem with Application in Smart Grid

We consider the problem of scheduling complex-valued demands over a discretized time horizon. Given a set of users, each user is associated with a set of demands representing different power consumption preferences. A demand is represented by a complex number, a time interval, and a utility value obtained if it is satisfied. At each time slot, the magnitude of the total selected demands should not exceed a given generation capacity. This naturally captures the supply constraints in alternating current (AC) electric systems. In this paper, we consider maximizing the aggregate user utility subject to power supply limits over a time horizon. We present approximation algorithms characterized by the maximum angle $ϕ$ between any two complex-valued demands. More precisely, a PTAS is presented for the case $ϕ\in [0,\tfracπ{2}]$, a bi-criteria FPTAS for $ϕ\in [0,π \mbox{-} \varepsilon]$ for any polynomially small $\varepsilon$, assuming the number of time slots in the discretized time horizon is a constant. Furthermore, if the number of time slots is part of the input, we present a reduction to the real-valued unsplittable flow problem on a path with only a constant approximation ratio. Finally, we present a practical greedy algorithm for the single time slot case with an approximation ratio of $\tfrac{1}{2}\cos \fracϕ{2}$ and a running time complexity of only ${O}(N\log N)$, $N$ standing for the aggregate number of user demands, which can be implemented efficiently in practice.

cs.DS↗
arXiv2017

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Sharing economy is a distributed peer-to-peer economic paradigm, which gives rise to a variety of social interactions for economic purposes. One fundamental distributed decision-making process is coalition formation for sharing certain replaceable resources collaboratively, for example, sharing hotel rooms among travelers, sharing taxi-rides among passengers, and sharing regular passes among users. Motivated by the applications of sharing economy, this paper studies a coalition formation game subject to the capacity of $K$ participants per coalition. The participants in each coalition are supposed to split the associated cost according to a given cost-sharing mechanism. A stable coalition structure is established when no group of participants can opt out to form another coalition that leads to lower individual payments. We quantify the inefficiency of distributed decision-making processes under a cost-sharing mechanism by the strong price of anarchy (SPoA), comparing a worst-case stable coalition structure and a social optimum. In particular, we derive SPoA for common fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games, and usage based cost-sharing). We show that the SPoA for equal-split, proportional-split, and usage based cost-sharing (under certain conditions) is $Θ(\log K)$, whereas the one for egalitarian and Nash bargaining solutions is $O(\sqrt{K} \log K)$. Therefore, distributed decision-making processes under common fair cost-sharing mechanisms induce only moderate inefficiency.

cs.GT↗
arXiv2017

Enumerating Vertices of $0/1$-Polyhedra associated with $0/1$-Totally Unimodular Matrices

We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron $\mathcal{P}(A,\mathbf{1})=\{x\in\RR^n \mid Ax\geq \b1,~x\geq \b0\}$, when $A$ is a totally unimodular matrix. Our algorithm is based on decomposing the hypergraph transversal problem for unimodular hypergraphs using Seymour's decomposition of totally unimodular matrices, and may be of independent interest.

cs.DS↗
arXiv2017

Drive Mode Optimization and Path Planning for Plug-in Hybrid Electric Vehicles

Drive modes are driver-selectable pre-set configurations of powertrain and certain vehicle parameters. Plug-in hybrid electric vehicles (PHEVs) typically feature special options of drive modes that can affect the hybrid energy source management system, for example, electric vehicle (EV) mode (that draws fully on battery) and charge sustaining (CS) mode (that utilizes internal combustion engine to charge battery while propelling the vehicle). This paper studies an optimization problem to enable the driver to select the appropriate drive modes for fuel minimization. We develop optimization algorithms that optimize the decisions of drive modes based on trip information, and integrated with path planning to find an optimal path, considering intermediate filling and charging stations. We further provide an online algorithm that is based on the revealed trip information. We evaluate our algorithms empirically on a Chevrolet Volt, which shows significant fuel savings.

cs.DS↗
arXiv2017

A Pseudo-Polynomial Algorithm for Mean Payoff Stochastic Games with Perfect Information and Few Random Positions

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph $G = (V, E)$, with local rewards $r: E \to \ZZ$, and three types of positions: black $V_B$, white $V_W$, and random $V_R$ forming a partition of $V$. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, or not, even when $|V_R|=0$. In fact, a pseudo-polynomial algorithm for BWR-games would already imply their polynomial solvability. In this paper, we show that BWR-games with a constant number of random positions can be solved in pseudo-polynomial time. More precisely, in any BWR-game with $|V_R|=O(1)$, a saddle point in uniformly optimal pure stationary strategies can be found in time polynomial in $|V_W|+|V_B|$, the maximum absolute local reward, and the common denominator of the transition probabilities.

cs.GT↗
arXiv2017

Finding Small Hitting Sets in Infinite Range Spaces of Bounded VC-dimension

We consider the problem of finding a small hitting set in an {\it infinite} range space $\cF=(Q,\cR)$ of bounded VC-dimension. We show that, under reasonably general assumptions, the infinite dimensional convex relaxation can be solved (approximately) efficiently by multiplicative weight updates. As a consequence, we get an algorithm that finds, for any $δ>0$, a set of size $O(s_{\cF}(z^*_\cF))$ that hits $(1-δ)$-fraction of $\cR$ (with respect to a given measure) in time proportional to $\log(\frac{1}δ)$, where $s_{\cF}(\frac{1}ε)$ is the size of the smallest $ε$-net the range space admits, and $z^*_{\cF}$ is the value of the {\it fractional} optimal solution. This {\it exponentially} improves upon previous results which achieve the same approximation guarantees with running time proportional to $\poly(\frac{1}δ)$. Our assumptions hold, for instance, in the case when the range space represents the {\it visibility} regions of a polygon in $\RR^2$, giving thus a deterministic polynomial time $O(\log z^*_{\cF})$-approximation algorithm for guarding $(1-δ)$-fraction of the area of any given simple polygon, with running time proportional to $\polylog(\frac{1}δ)$.

cs.CG↗
arXiv2016

Optimal Power Flow with Inelastic Demands for Demand Response in Radial Distribution Networks

The classical optimal power flow problem optimizes the power flow in a power network considering the associated flow and operating constraints. In this paper, we investigate optimal power flow in the context of utility-maximizing demand response management in distribution networks, in which customers' demands are satisfied subject to the operating constraints of voltage and transmission power capacity. The prior results concern only elastic demands that can be partially satisfied, whereas power demands in practice can be inelastic with binary control decisions, which gives rise to a mixed integer programming problem. We shed light on the hardness and approximability by polynomial-time algorithms for optimal power flow problem with inelastic demands. We show that this problem is inapproximable for general power network topology with upper and lower bounds of nodal voltage. Then, we propose an efficient algorithm for a relaxed problem in radial networks with bounded transmission power loss and upper bound of nodal voltage. We derive an approximation ratio between the proposed algorithm and the exact optimal solution. Simulations show that the proposed algorithm can produce close-to-optimal solutions in practice.

cs.DS↗
arXiv2016

Truthful Mechanisms for Combinatorial Allocation of Electric Power in Alternating Current Electric Systems for Smart Grid

Traditional studies of combinatorial auctions often only consider linear constraints. The rise of smart grid presents a new class of auctions, characterized by quadratic constraints. This paper studies the {\em complex-demand knapsack problem}, in which the demands are complex valued and the capacity of supplies is described by the magnitude of total complex-valued demand. This naturally captures the power constraints in alternating current (AC) electric systems. In this paper, we provide a more complete study and generalize the problem to the multi-minded version, beyond the previously known $\frac{1}{2}$-approximation algorithm for only a subclass of the problem. More precisely, we give a truthful PTAS for the case $ϕ\in[0,\fracπ{2}-δ]$, and a truthful FPTAS, which {\it fully} optimizes the objective function but violates the capacity constraint by at most $(1+ε)$, for the case $ϕ\in(\fracπ{2},π-δ]$, where $ϕ$ is the maximum argument of any complex-valued demand and $ε,δ>0$ are arbitrarily small constants. We complement these results by showing that, unless P=NP, neither a PTAS for the case $ϕ\in(\fracπ{2},π-δ]$ nor any bi-criteria approximation algorithm with polynomial guarantees for the case when $ϕ$ is arbitrarily close to $π$ (that is, when $δ$ is arbitrarily close to $0$) can exist.

cs.GT↗