Khaled Elbassioni

Khaled Elbassioni
Max Planck Institute for Chemical Energy Conversion | MPIBAC

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195
Publications
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2,162
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Publications

Publications (195)
Article
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We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. Assuming the existence of an integrality gap verifier with a bounded approximation guarantee for the LP relaxation of the non-robust version of the problem, we derive approximation algorithms for the robust version under different types...
Chapter
Full-text available
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 have been proposed that utilize the particular structure of this class of problems in order to obtain more efficient algorithms than those offered by gene...
Article
In this paper, we consider a distributed joint sensing and communication (DJSC) system in which each radar sensor as a JSC node is equipped with a sensing function and a communication function. Deploying multiple JSC nodes may require a large amount of bandwidth. Therefore, we investigate the bandwidth allocation problem for the DJSC system. In par...
Preprint
Full-text available
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...
Article
We consider the problem of pricing edges of a line graph so as to maximize the profit made from selling intervals to single-minded customers. An instance is given by a set E of n edges with a limited supply for each edge, and a set of m clients, where each client specifies one interval of E she is interested in and a budget B j which is the maximum...
Preprint
Full-text available
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\subse...
Article
Binary non-linear programs belong to the class of combinatorial problems which are computationally hard even to approximate. This paper aims to explore some conditions on the problem structure, under which the resulting problem can be well approximated. Particularly, we consider a setting when both objective function and constraint are low-rank fun...
Article
The placement of phasor measurement units (PMUs) in modern power systems provides improved monitoring and control characteristics of the entire electrical network. Nevertheless, the installation of additional PMU devices is associated with relatively high cost and complicated communication infrastructure. As a result, the allocation of the PMU devi...
Article
Full-text available
A routine task faced by Microgrid (MG) operators is to optimally allocate incoming power demand requests while accounting for the underlying power distribution network and the associated constraints. Typically, this has been formulated as an offline optimization problem for day-ahead scheduling, assuming perfect forecasting of the demands. In pract...
Article
Full-text available
Given a CNF formula Φ with clauses C1,…,Cm and variables V={x1,…,xn}, a truth assignment a:V→{0,1} of Φ leads to a clause sequence σΦ(a)=(C1(a),…,Cm(a))∈{0,1}m where Ci(a)=1 if clause Ci evaluates to 1 under assignment a, otherwise Ci(a)=0. The set of all possible clause sequences carries a lot of information on the formula, e.g. SAT, MAX-SAT and M...
Preprint
Coalition formation is a central part of social interactions. In the emerging era of social peer-to-peer interactions (e.g., sharing economy), coalition formation will be often carried out in a decentralized manner, based on participants' individual preferences. A likely outcome will be a stable coalition structure, where no group of participants c...
Preprint
Given a partially order set (poset) $P$, and a pair of families of ideals $\cI$ and filters $\cF$ in $P$ such that each pair $(I,F)\in \cI\times\cF$ has a non-empty intersection, the dualization problem over $P$ is to check whether there is an ideal $X$ in $P$ which intersects every member of $\cF$ and does not contain any member of $\cI$. Equivale...
Article
This paper proposes a novel unified prediction approach for both small-signal and transient rotor angle stability as opposed to other studies that have only addressed transient rotor angle stability. Deep learning techniques are employed in this paper to train an online prediction model for rotor angle stability (RAS) using the voltage phasor measu...
Article
Full-text available
The massive size of single cell RNA sequencing datasets often exceeds the capability of current computational analysis methods to solve routine tasks such as detection of cell types. Recently, geometric sketching was introduced as an alternative to uniform subsampling. It selects a subset of cells (the sketch) that evenly cover the transcriptomic s...
Preprint
Full-text available
Given a CNF formula $\Phi$ with clauses $C_1,\ldots,C_m$ and variables $V=\{x_1,\ldots,x_n\}$, a truth assignment $a:V\rightarrow\{0,1\}$ of $\Phi$ leads to a clause sequence $\sigma_\Phi(a)=(C_1(a),\ldots,C_m(a))\in\{0,1\}^m$ 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 c...
Article
The Internet-of-Things (IoT) has engendered a new paradigm of integrated sensing and actuation systems for intelligent monitoring and control of smart homes and buildings. One viable manifestation is that of IoT-empowered smart lighting systems, which rely on the interplay between smart light bulbs (equipped with controllable LED devices and wirele...
Article
The AC Optimal power flow (OPF) problem is one of the most fundamental problems in power systems engineering. For the past decades, researchers have been relying on unproven heuristics to tackle OPF. The hardness of OPF stems from two issues: (1) non-convexity and (2) combinatoric constraints (e.g., discrete power extraction constraints). The recen...
Article
Full-text available
Stimulated by salient applications arising from power systems, this paper studies a class of non-linear Knapsack problems with non-separable quadratic constrains, formulated in either binary or integer form. These problems resemble the duals of the corresponding variants of 2-weighted Knapsack problem (a.k.a., complex-demand Knapsack problem) which...
Preprint
We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be used to derive approximation algorithms for the robust version.
Conference Paper
Full-text available
P2P (peer-to-peer) energy sharing allows household users to share their local energy resources (e.g., rooftop PVs, home batteries) based on an agreed cost-sharing mechanism (e.g., implemented as a smart contract over a blockchain ledger). Sharing energy resources is becoming a new form of sharing economy. This not only promotes renewable energy ado...
Article
Full-text available
We consider the following semi-infinite linear programming problems: max (resp., min) cTx s.t. yTAix+(di)Tx≤bi (resp., yTAix+(di)Tx≥bi), for all y∈Yi, for i=1,…,N, where Yi⊆R+m are given compact convex sets and Ai∈R+mi×n, b=(b1,…bN)∈R+N, di∈R+n, and c∈R+n are given non-negative matrices and vectors. This general framework is useful in modeling many...
Preprint
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...
Article
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→Z, 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...
Preprint
Full-text available
Single-cell RNA sequencing enables the construction of trajectories describing the dynamic changes in gene expression underlying biological processes such as cell differentiation and development. The comparison of single-cell trajectories under two distinct conditions can illuminate the differences and similarities between the two and can thus be a...
Conference Paper
The interplay of smart light bulbs (equipped with wireless controllable LEDs) and mobile sensors (embedded in wearable devices, such as smart watches and spectacles) enables a wide range of interactive lighting applications. One notable example is a smart lighting control system that provides automated illuminance management by wearable sensors clo...
Article
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...
Preprint
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 solv...
Article
We consider the problem of enumerating all minimal hitting sets of a given hypergraph (V,R), where V is a finite set, called the vertex set and R is a set of subsets of V called the hyperedges. We show that, when the hypergraph admits a balanced subdivision, then a recursive decomposition can be used to obtain efficiently all minimal hitting sets o...
Conference Paper
To meet the substantial demand for electrified transportation, a high level of penetration of electric vehicles (EVs) will be expected to incur considerable impacts on the reliability of electricity grid. Hence, there requires an intelligent scheduling mechanism for EV charging for maintaining the electricity grid within the operating limits and ab...
Conference Paper
To cope with the high-level penetration of electric vehicles (EVs), an intelligent scheduling mechanism for EV charging is required for maintaining the electricity grid within the operating limits, mitigating the demand peaks, and maximizing the benefit of intermittent renewable energy. This paper studies the scheduling optimization problem of EV c...
Article
Full-text available
We consider finite Markov decision processes with undiscounted total effective payoff. We show that there exist uniformly optimal pure and stationary strategies that can be computed by solving a polynomial number of linear programs. This implies that in a two-player zero-sum stochastic game with perfect information and with total effective payoff t...
Article
Our ever-increasing reliance on electricity coupled with inefficient consumption has resulted in several economical and environmental threats. To curb these threats, smart grids are emerging. These improved power systems could potentially reduce the peak consumption and better match demand to supply, to produce both economical and environmental adv...
Article
Full-text available
We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$-ergodic, if its values from any two initial positions differ by at most $\epsilon$. The proposed new algorithm outputs for every $\epsilon>0$ in finite time ei...
Book
The electric power grid which has been an indispensable part of our society is being put under increasing pressure to meet the demands of a major surge in global energy consumption. As a result, the power grid needs to undergo transformations to meet the new challenges for a more sustainable society. One of these transformations is the need for con...
Article
The list update problem is a well studied online problem in the area of self-adjusting data structures. Understanding the o?ine version of this problem is crucial because of the role it plays in the competitive analysis of online list update algorithms. In this paper we settle a long-standing open problem by showing that the o?ine list update probl...
Article
Full-text available
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-...
Article
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 un...
Article
The aim of this paper is to study approximation algorithms for a class of binary packing problems with quadratic constraints, where the constraint matrices are completely positive and have low cp-rank. We show that limiting the cp-rank makes the quadratic optimization problem exhibit similar approximability behavior as the linear case, assuming a c...
Conference Paper
We consider the following semi-infinite linear programming problems: \(\max \) (resp., \(\min \)) \(c^Tx\) s.t. \(y^TA_ix+(d^i)^Tx \le b_i\) (resp., \(y^TA_ix+(d^i)^Tx \ge b_i)\), for all \(y \in \mathcal Y_i\), for \(i=1,\ldots ,N\), where \(\mathcal Y_i\subseteq \mathbb {R}^{m_i}_+\) are given compact convex sets and \(A_i\in \mathbb {R}^{m_i\tim...
Article
Full-text available
R. Lavi and C. Swamy (FOCS 2005, J. ACM 58(6), 25, 2011) introduced a general method for obtaining truthful-in-expectation mechanisms from linear programming based approximation algorithms. Due to the use of the Ellipsoid method, a direct implementation of the method is unlikely to be efficient in practice. We propose to use the much simpler and us...
Article
Full-text available
Minimizing the peak power consumption and matching demand to supply, under fixed threshold polices, are two key requirements for the success of the future electricity market. In this work, we consider dynamic pricing methods to minimize the peak load and match demand to supply in the smart grid. As these optimization problems are computationally ha...
Article
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, fo...
Article
This paper investigates computing completely positive (cp) decompositions of positive semi-definite (PSD) matrices, a problem which arises in many applications. We propose the first polynomial-time algorithm for checking if a given PSD matrix has cp-rank of at most r, when r is a given constant. In addition, we present a polynomial-time algorithm f...
Conference Paper
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 user’s preferences. A demand is represented by a complex number, a time interval, and a utility value obtained if the demand is satisfied. At each time slot, the mag...
Article
We consider Gillette’s two-person zero-sum stochastic games with perfect information. For each (Formula presented.) we introduce an effective reward function, called k-total. For (Formula presented.) and 1 this function is known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case. For all k, we prove t...
Article
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...
Article
The first step in the analysis of data produced by ultra-high-throughput next-generation sequencing technology is to map short sequence "reads" to a reference genome, if available. Sequencing errors, repeat regions, and polymorphisms may lead a read to align to multiple locations in the genome reasonably well. While ignoring such multimapping reads...
Article
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 solution. A stable coalition structure is established, when no group of participants can opt out to form another coalition that leads...
Article
In 1964 Shapley observed that a matrix has a saddle point in pure strategies whenever every its (Formula presented.) submatrix has one. In contrast, a bimatrix game may have no pure strategy Nash equilibrium (NE) even when every (Formula presented.) subgame has one. Nevertheless, Shapley’s claim can be extended to bimatrix games as follows. We part...
Conference Paper
Motivated by the power allocation problem in AC (alternating current) electrical systems, we study the multi-objective (combinatorial) optimization problem where a constant number of (nonnegative) linear functions are simultaneously optimized over a given feasible set of 0–1 points defined by quadratic constraints. Such a problem is very hard to so...
Article
Full-text available
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 complex-demand knapsack problem, in which the demands are complex-valued and the capacity of supplies is described by the magnitude of total com...
Article
We consider finite Markov decision processes (MDPs) with undiscounted total effective payoff. We show that there exist uniformly optimal pure stationary strategies that can be computed by solving a polynomial number of linear programs. We apply this result to two-player zero-sum stochastic games with perfect information and undiscounted total effec...
Conference Paper
We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real \(\epsilon \), let us call a stochastic game \(\epsilon \)-ergodic, if its values from any two initial positions differ by at most \(\epsilon \). The proposed new algorithm outputs for every \(\epsilon >0\) in fi...
Article
Full-text available
We consider Gillette's two-person zero-sum stochastic games with perfect information. For each $k \in \mathbb{Z}_+$ we introduce a payoff function, called the $k$-total reward. For $k = 0$ and $1$ these payoffs are known as mean payoff and total reward, respectively. We restrict our attention to the deterministic case, the so called cyclic games. F...
Article
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient approximation algorithms for their solutions. The purpose of this paper is to investigate the approximability for a...
Article
The computation of transversal hypergraphs in output-polynomial time is a long standing open question. An Apriori-like level-wise approach referred to as the HBC-algorithm or MTminer was published in 2007 by Hébert, Bretto, and Crémilleux [A Data Mining Formalization to Improve Hypergraph Minimal Transversal Computation, Fundamenta Informaticae, 80...
Conference Paper
Full-text available
R. Lavy and C. Swamy (FOCS 2005, J. ACM 2011) introduced a general method for obtaining truthful-in-expectation mechanisms from linear programming based approximation algorithms. Due to the use of the Ellipsoid method, a direct implementation of the method is unlikely to be efficient in practice. We propose to use the much simpler and usually faste...
Conference Paper
A challenge in future smart grid is how to efficiently allocate power among customers considering inelastic demands, when the power supply is constrained by the network or generation capacities. This problem is an extension to the classical knapsack problem in a way that the item values are expressed as non-positive real or complex numbers represen...
Conference Paper
Full-text available
Traditional studies of combinatorial auctions often only consider linear constraints (by which the demands for certain goods are limited by the corresponding supplies). The rise of smart grid presents a new class of auctions, characterized by quadratic constraints. Yu and Chau [AAMAS 13'] introduced the "complex-demand knapsack problem", in which t...
Conference Paper
Full-text available
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 → ℝ, and three types of vertices: 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, o...
Article
It is shown that the discount factor needed to solve an undiscounted mean payoff stochastic game to optimality is exponentially close to 1, even in one-player games with a single random node and polynomially bounded rewards and transition probabilities. For the class of the so-called irreducible games with perfect information and a constant number...
Article
We consider two-person zero-sum mean payoff undiscounted stochastic games and obtain sufficient conditions for the existence of a saddle point in uniformly optimal stationary strategies. Namely, these conditions enable us to bring the game, by applying potential transformations, to a canonical form in which locally optimal strategies are globally o...
Article
Abstract Molecular simulation techniques are increasingly being used to study biomolecular systems at an atomic level. Such simulations rely on empirical force fields to represent the intermolecular interactions. There are many different force fields available-each based on a different set of assumptions and thus requiring different parametrization...
Conference Paper
Full-text available
Given two bounded convex sets X ⊆ ℝm and Y ⊆ ℝn , specified by membership oracles, and a continuous convex-concave function F:X×Y → ℝ, we consider the problem of computing an ε-approximate saddle point, that is, a pair (x *,y *) ∈ X×Y such that \(\sup_{y\in Y} F(x^*,y)\le \inf_{x\in X}F(x,y^*)+\varepsilon .\) Grigoriadis and Khachiyan (1995), based...
Article
In this paper, we consider the 1.5D terrain guarding problem in which every point on the terrain that is to be covered has an integer demand associated with it. The goal is to find a minimum cardinality set of guards such that each point is guarded by a number of guards satisfying its demand. We present a first constant-factor approximation algorit...
Article
In the highway problem, we are given a path, and a set of buyers interested in buying sub-paths of this path; each buyer declares a non-negative budget, which is the maximum amount of money she is willing to pay for that sub-path. The problem is to assign non-negative prices to the edges of the path such that we maximize the profit obtained by sell...
Conference Paper
We consider the problem of pricing edges of a line graph so as to maximize the profit made from selling intervals to single-minded customers. An instance is given by a set E of n edges with a limited supply for each edge, and a set of m clients, where each client j specifies one interval of E she is interested in and a budget B j which is the maxim...
Article
We report that the Connected Set Cover (CSC) problem is just a special case of the Group Steiner Tree (GST) problem. Based on that we obtain the first algorithm for CSC with polylogarithmic approximation guarantee as well as the first approximation algorithms for the weighted version of the problem and the version with requirements. Moreover, we ar...
Article
In the unlimited-supply profit-maximizing pricing problem, we are given the consumers ’ consideration sets and know their purchase strategy (e.g. buy the cheapest items). The goal is to price the items to maximize the revenue. Previous studies suggest that this problem is too general to obtain even a sublinear approximation ratio (in terms of the n...
Conference Paper
Full-text available
We give a very simple approximation algorithm for the maximum asymmetric traveling salesman problem. The approximation guarantee of our algorithm is 2/3, which matches the best known approximation guarantee by Kaplan, Lewenstein, Shafrir and Sviridenko. Our algorithm is simple to analyze, and contrary to previous approaches, which need an optimal s...
Article
We consider nn-person positional games with perfect information modeled by finite directed graphs that may have directed cycles, assuming that all infinite plays form a single outcome cc, in addition to the standard outcomes a1,…,ama1,…,am formed by the terminal positions. (For example, in the case of Chess or Backgammon n=2n=2 and cc is a draw.) T...
Article
Consider the following toy problem. There are $m$ rectangles and $n$ points on the plane. Each rectangle $R$ is a consumer with budget $B_R$, who is interested in purchasing the cheapest item (point) inside R, given that she has enough budget. Our job is to price the items to maximize the revenue. This problem can also be defined on higher dimensio...
Article
Full-text available
We show that finding the simplices containing a fixed given point among those defined on a set of n points can be done in O(n + k) time for the two-dimensional case, and in O(n ² + k) time for the three-dimensional case, where k is the number of these simplices. As a byproduct, we give an alternative (to the algorithm in Ref. 4) O(n log r) algorith...
Conference Paper
Golumbic et al. (Discrete Appl. Math. 154:1465–1477, 2006) defined the readability of a monotone Boolean function f to be the minimum integer k such that there exists an ∧−∨-formula equivalent to f in which each variable appears at most k times. They asked whether there exists a polynomial-time algorithm, which given a monotone Boolean function f,...
Article
Given a graph G=(V,E) and a weight function on the edges w:E→ℝ, we consider the polyhedron P(G,w) of negative-weight flows on G, and get a complete characterization of the vertices and extreme directions of P(G,w). Based on this characterization, and using a construction developed in Khachiyan et al. (Discrete Comput. Geom. 39(1–3):174–190, 2008),...
Conference Paper
Full-text available
In this paper, we consider two-player zero-sum stochastic mean payoff games with perfect information modeled by a digraph with black, white, and random vertices. These BWR-games games are polynomially equivalent with the classical Gillette games, which include many well-known subclasses, such as cyclic games, simple stochastic games, stochastic par...