arXiv subjects

Khaled Elbassioni

Publications and source records attributed to Khaled Elbassioni.

At least 19 recordsLinked to original sources

arXiv2026

Random Garbage Separates XOR from Forward-Only Queries

We give exponential quantum query separations between the standard XOR interface and two forward-only interfaces that supply neither an adjoint nor an inverse oracle. Let $X=\F_2^n$, $N=|X|$, and $f_{h,r}(x)=(h(x),x,r_x)$, where $h:X\to X$ is promised to be either a permutation or a Simon two-to-one function, and $r$ is a fixed table of $n$-bit tags, unrestricted by the promise and reused on every query. The resulting problem is solvable with at most $n+2$ standard XOR queries, but has forward-erasing query complexity $\Theta(\sqrt N)$. This answers affirmatively open question 11 in [Scott Aaronson. Open problems related to quantum query complexity. ACM Transactions on Quantum Computing, 2(4):14:1-14:9, 2021] . We also embed these instances into permutations. The detailed construction retains the copy of $x$ in each prescribed output, but for these promises that copy can be replaced by one bit that distinguishes the two inputs in every Simon pair. This gives a permutation domain of size $L=4N^2$ and a permutation problem with the same standard-query upper bound and forward-only in-place query complexity $\Theta(\sqrt N)=\Theta(L^{1/4})$. Both lower bounds remain valid with a clean coherent bypass. The common lower bound uses an analysis-only recording replacement. In the replacement computation, tracing out the fixed random tag table after $T$ calls gives a sum of positive-semidefinite operator contributions, each depending on $h$ at no more than $T$ addresses. On such a set, the restrictions induced by random permutations and random Simon functions differ only if the set contains a hidden Simon pair, an event of probability $O(T^2/N)$.

cs.CC↗

arXiv2026

Tight UGC Thresholds for Geometric Stabbing Problems

Many geometric stabbing problems admit natural covering LPs in which each constraint is a union of consecutive traces on ordered candidate sets. We prove a transfer theorem showing that every fixed finite, bounded-arity integrality-gap instance of this form yields a matching hardness ratio under the Unique Games Conjecture. Using the strict-CSP framework of Kumar, Manokaran, Tulsiani, and Vishnoi [SODA 2011], we construct the required connected local distributions by randomized rounding and a full-support perturbation. Given a fractional vector $x$ on a block, the rounding selects candidate $i$ with marginal probability $x_i$ and hits each consecutive trace $T$ with probability $\min\{1,x(T)\}$. We obtain three tight UGC thresholds. First, for every fixed $d\ge 2$, stabbing arbitrary-size axis-parallel $d$-cubes with coordinate hyperplanes has threshold $d$. For $d=2$, the hardness holds for arbitrary-size squares and establishes threshold $2$ for rectangle and square stabbing, matching the $2$-approximation of Gaur, Ibaraki, and Krishnamurti [ESA 2000]. Second, stabbing horizontal segments with horizontal and vertical lines has threshold $e/(e-1)$, matching the $e/(e-1)$-approximation of Kovaleva and Spieksma [ESA 2004]. Third, separated $d$-interval transversal has threshold $d$ for every fixed $d\ge 2$, closing under UGC the gap left by the $d$-approximation of Ben-David, Grant, Ma, and Sharpe [CCCG 2012].

cs.CG↗

arXiv2025

A Deterministic Bicriteria Approximation Algorithm for the Art Gallery Problem

Given a polygon $H$ in the plane, the art gallery problem calls for fining the smallest set of points in $H$ from which every other point in $H$ is seen. We give a deterministic algorithm that, given any polygon $H$ with $h$ holes, $n$ rational veritces of maximum bit-length $L$, and a parameter $\delta \in(0,1)$, is guaranteed to find a set of points in $H$ of size $O\big(\OPT\cdot\log(h+2)\cdot\log (\OPT\cdot\log(h+2)))$ that sees at least a $(1-\delta)$-fraction of the area of the polygon. The running time of the algorithm is polynomial in $h$, $n$, $L$ and $\log(\frac{1}{\delta})$, where $\OPT$ is the size of an optimum solution.

cs.CG↗

arXiv2025

Online Multiple Resource Allocation Problems with Departures via the Primal-Dual Approach

In this paper we propose primal-dual algorithms for different variants of the online resource allocation problem with departures. In the basic variant, requests (items) arrive over time to a set of resources (knapsacks) and upon arrival, the duration of time a request may occupy a resource, the demand and reward if the request can be granted, become known. %We assume that the duration of stay of a request may depend on the resource. %and that resources may have different capacity sizes. The goal of the algorithm is to decide whether to accept/reject a request upon arrival and to which resource to allocate it such that the reward obtained over time is maximized. Under some mild assumptions, we show that the proposed primal-dual algorithm achieves a competitive ratio of $O\big(\log(\barθ^{\max}\cdot\bar d^{\max})\big)$, where $\bar θ^{\max}$ is the maximum value density fluctuation ratio and $\bar d^{\max}$ is the maximum duration fluctuation ratio. We prove similar results for two other variants, namely, one with an additional load balancing constraint, and the multi-dimensional variant where an admitted request consumes capacity on multiple resources. Our results show that the primal-dual approach offers a simple, unified framework for obtaining competitive ratios comparable to those previously obtained via threshold policies known for these problems. Additionally, we show that this framework allows us to incorporate additional constraints, such as load-balancing constraints, without sacrificing the competitive ratio.

cs.DS↗

arXiv2025

Collaborative Last-Mile Delivery: A Multi-Platform Vehicle Routing Problem With En-route Charging

The rapid growth of e-commerce and the increasing demand for timely, cost-effective last-mile delivery have increased interest in collaborative logistics. This research introduces a novel collaborative synchronized multi-platform vehicle routing problem with drones and robots (VRP-DR), where a fleet of $\mathcal{M}$ trucks, $\mathcal{N}$ drones and $\mathcal{K}$ robots, cooperatively delivers parcels. Trucks serve as mobile platforms, enabling the launching, retrieving, and en-route charging of drones and robots, thereby addressing critical limitations such as restricted payload capacities, limited range, and battery constraints. The VRP-DR incorporates five realistic features: (1) multi-visit service per trip, (2) multi-trip operations, (3) flexible docking, allowing returns to the same or different trucks (4) cyclic and acyclic operations, enabling return to the same or different nodes; and (5) en-route charging, enabling drones and robots to recharge while being transported on the truck, maximizing operational efficiency by utilizing idle transit time. The VRP-DR is formulated as a mixed-integer linear program (MILP) to minimize both operational costs and makespan. To overcome the computational challenges of solving large-scale instances, a scalable heuristic algorithm, FINDER (Flexible INtegrated Delivery with Energy Recharge), is developed, to provide efficient, near-optimal solutions. Numerical experiments across various instance sizes evaluate the performance of the MILP and heuristic approaches in terms of solution quality and computation time. The results demonstrate significant time savings of the combined delivery mode over the truck-only mode and substantial cost reductions from enabling multi-visits. The study also provides insights into the effects of en-route charging, docking flexibility, drone count, speed, and payload capacity on system performance.

cs.MA↗

arXiv2025

Two-person Positive Shortest Path Games Have Nash Equilibria in Pure Stationary Strategies

We prove that every finite two-person shortest path game, where the local cost of every move is positive for each player, has a Nash equilibrium (NE) in pure stationary strategies, which can be computed in polynomial time. We also extend the existence result to infinite graphs with finite out-degrees. Moreover, our proof gives that a terminal NE (in which the play is a path from the initial position to a terminal) exists provided at least one of the two players can guarantee reaching a terminal. If none of the players can do it, in other words, if each of the two players has a strategy that separates all terminals from the initial position $s$, then, obviously, a cyclic NE exists, although its cost is infinite for both players, since we restrict ourselves to positive games. We conjecture that a terminal NE exists too, provided there exists a directed path from $s$ to a terminal. However, this is open. We extend our result to short paths interdiction games, where at each vertex, we allow one player to block some of the arcs and the other player to choose one of the non-blocked arcs. Assuming that blocking sets are chosen from an independence system given by an oracle, we give an algorithm for computing a NE in time $O(|E|(\log|V|+τ))$, where $V$ is the set of vertices, $E$ is the set of arcs, and $τ$ is the maximum time taken by the oracle on any input.

cs.DM↗

arXiv2024

Dual Bounded Generation: Polynomial, Second-order Cone and Positive Semidefinite Matrix Inequalities

In the monotone integer dualization problem, we are given two sets of vectors in an integer box such that no vector in the first set is dominated by a vector in the second. The question is to check if the two sets of vectors cover the entire integer box by upward and downward domination, respectively. It is known that the problem is (quasi-)polynomially equivalent to that of enumerating all maximal feasible solutions of a given monotone system of linear/separable/supermodular inequalities over integer vectors. The equivalence is established via showing that the dual family of minimal infeasible vectors has size bounded by a (quasi-)polynomial in the sizes of the family to be generated and the input description. Continuing in this line of work, in this paper, we consider systems of polynomial, second-order cone, and semidefinite inequalities. We give sufficient conditions under which such bounds can be established and highlight some applications.

cs.DM↗

arXiv2024

Informational Rescaling of PCA Maps with Application to Genetic Distance

We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component analysis (PCA) (when the variables are asymptotically Gaussian) into an entropy-based map where distances are based on mutual information (MI). Rescaling Principal Component based distances using MI allows a representation of relative statistical associations when, as in genetics, it is applied on bit measurements between individuals' genomic mutual information. This entropy rescaled PCA, while preserving order relationships (along a dimension), changes the relative distances to make them linear to information. We show the effect on the entire world population and some subsamples, which leads to significant differences with the results of current research.

cs.IT↗

arXiv2023

Improved Approximation Guarantees for Power Scheduling Problems With Sum-of-Squares Constraints

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum of squares of linear functions. Its nonlinear nature adds complexity to the scheduling problem, rendering it notably challenging, even in the case of a linear objective. In fact, exact polynomial time algorithms are unlikely to exist, and thus, prior works have focused on designing approximation algorithms with polynomial running time and provable guarantees on the solution quality. In an effort to advance this line of research, we present novel approximation algorithms yielding significant improvements over the existing state-of-the-art results for these problems.

cs.DS↗

arXiv2023

DClEVerNet: Deep Combinatorial Learning for Efficient EV Charging Scheduling in Large-scale Networked Facilities

With the electrification of transportation, the rising uptake of electric vehicles (EVs) might stress distribution networks significantly, leaving their performance degraded and stability jeopardized. To accommodate these new loads cost-effectively, modern power grids require coordinated or ``smart'' charging strategies capable of optimizing EV charging scheduling in a scalable and efficient fashion. With this in view, the present work focuses on reservation management programs for large-scale, networked EV charging stations. We formulate a time-coupled binary optimization problem that maximizes EV users' total welfare gain while accounting for the network's available power capacity and stations' occupancy limits. To tackle the problem at scale while retaining high solution quality, a data-driven optimization framework combining techniques from the fields of Deep Learning and Approximation Algorithms is introduced. The framework's key ingredient is a novel input-output processing scheme for neural networks that allows direct extrapolation to problem sizes substantially larger than those included in the training set. Extensive numerical simulations based on synthetic and real-world data traces verify the effectiveness and superiority of the presented approach over two representative scheduling algorithms. Lastly, we round up the contributions by listing several immediate extensions to the proposed framework and outlining the prospects for further exploration.

cs.LG↗

arXiv2023

Joint Rate Allocation and Power Control for RSMA-Based Communication and Radar Coexistence Systems

We consider a rate-splitting multiple access (RSMA)-based communication and radar coexistence (CRC) system. The proposed system allows an RSMA-based communication system to share spectrum with multiple radars. Furthermore, RSMA enables flexible and powerful interference management by splitting messages into common parts and private parts to partially decode interference and partially treat interference as noise. The RSMA-based CRC system thus significantly improves spectral efficiency, energy efficiency and quality of service (QoS) of communication users (CUs). However, the RSMA-based CRC system raises new challenges. Due to the spectrum sharing, the communication network and the radars cause interference to each other, which reduces the signal-to-interference-plus-noise ratio (SINR) of the radars as well as the data rate of the CUs in the communication network. Therefore, a major problem is to maximize the sum rate of the CUs while guaranteeing their QoS requirements of data transmissions and the SINR requirements of multiple radars. To achieve these objectives, we formulate a problem that optimizes i) the common rate allocation to the CUs, transmit power of common messages and transmit power of private messages of the CUs, and ii) transmit power of the radars. The problem is non-convex with multiple decision parameters, which is challenging to be solved. We propose two algorithms. The first sequential quadratic programming (SQP) can quickly return a local optimal solution, and has been known to be the state-of-the-art in nonlinear programming methods. The second is an additive approximation scheme (AAS) which solves the problem globally in a reasonable amount of time, based on the technique of applying exhaustive enumeration to a modified instance. The simulation results show the improvement of the AAS compared with the SQP in terms of sum rate.

cs.IT↗

arXiv2022

Approximations for Generalized Unsplittable Flow on Paths with Application to Power Systems Optimization

The Unsplittable Flow on a Path (UFP) problem has garnered considerable attention as a challenging combinatorial optimization problem with notable practical implications. Steered by its pivotal applications in power engineering, the present work formulates a novel generalization of UFP, wherein demands and capacities in the input instance are monotone step functions over the set of edges. As an initial step towards tackling this generalization, we draw on and extend ideas from prior research to devise a quasi-polynomial time approximation scheme (QPTAS) under the premise that the demands and capacities lie in a quasi-polynomial range. Second, retaining the same assumption, an efficient logarithmic approximation is introduced for the single-source variant of the problem. Finally, we round up the contributions by designing a (kind of) black-box reduction that, under some mild conditions, allows to translate LP-based approximation algorithms for the studied problem into their counterparts for the Alternating Current Optimal Power Flow (AC OPF) problem -- a fundamental workflow in operation and control of power systems.

cs.DS↗

arXiv2022

On Dualization over Distributive Lattices

Given a partially order set (poset) $P$, and a pair of families of ideals $\mathcal{I}$ and filters $\mathcal{F}$ in $P$ such that each pair $(I,F)\in \mathcal{I}\times\mathcal{F}$ 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 $\mathcal{F}$ and does not contain any member of $\mathcal{I}$. Equivalently, the problem is to check for a distributive lattice $L=L(P)$, given by the poset $P$ of its set of joint-irreducibles, and two given antichains $\mathcal{A},\mathcal{B}\subseteq L$ such that no $a\in\mathcal{A}$ is dominated by any $b\in\mathcal{B}$, whether $\mathcal{A}$ and $\mathcal{B}$ cover (by domination) the entire lattice. We show that the problem can be solved in quasi-polynomial time in the sizes of $P$, $\mathcal{A}$ and $\mathcal{B}$, thus answering an open question in Babin and Kuznetsov (2017). As an application, we show that minimal infrequent closed sets of attributes in a rational database, with respect to a given implication base of maximum premise size of one, can be enumerated in incremental quasi-polynomial time.

cs.DM↗

arXiv2022

Approximately Socially-Optimal Decentralized Coalition Formation with Application to P2P Energy Sharing

The paradigm of P2P (peer-to-peer) economy has emerged in diverse areas. "P2P energy sharing" is a new form of P2P economy in the energy sector, which allows users to establish longer-term sharing arrangements of their local energy resources (e.g., rooftop PVs, home batteries) with joint optimized energy management. In such a P2P setting, a coalition of users is formed for sharing resources in a decentralized manner by self-interested users based on their individual preferences. A likely outcome of decentralized coalition formation will be a stable coalition structure, where no group of users could cooperatively opt out to form another coalition that induces higher preferences to all its members. Remarkably, there exist a number of fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games) that model practical cost-sharing applications with desirable properties, such as the existence of a stable coalition structure with a small strong price-of-anarchy (SPoA) to approximate the social optimum. In this paper, we provide general results of decentralized coalition formation: (1) We establish a logarithmic lower bound on SPoA, and hence, show several previously known fair cost-sharing mechanisms are the best practical mechanisms with minimal SPoA. (2) We show that the SPoA of egalitarian and Nash bargaining cost-sharing mechanisms to match the lower bound. (3) We derive the SPoA of a mix of different cost-sharing mechanisms. (4) We present a decentralized algorithm to form a stable coalition structure. (5) Finally, we apply our general results to P2P energy sharing and present an empirical study of decentralized coalition formation in a real-world project. We study the empirical SPoA, which is observed within 95% of the social optimal cost with coalitions of 2 and 3 users, via fair cost-sharing mechanisms.

cs.GT↗

arXiv2022

Autonomous Recharging and Flight Mission Planning for Battery-operated Autonomous Drones

Unmanned aerial vehicles (UAVs), commonly known as drones, are being increasingly deployed throughout the globe as a means to streamline monitoring, inspection, mapping, and logistic routines. When dispatched on autonomous missions, drones require an intelligent decision-making system for trajectory planning and tour optimization. Given the limited capacity of their onboard batteries, a key design challenge is to ensure the underlying algorithms can efficiently optimize the mission objectives along with recharging operations during long-haul flights. With this in view, the present work undertakes a comprehensive study on automated tour management systems for an energy-constrained drone: (1) We construct a machine learning model that estimates the energy expenditure of typical multi-rotor drones while accounting for real-world aspects and extrinsic meteorological factors. (2) Leveraging this model, the joint program of flight mission planning and recharging optimization is formulated as a multi-criteria Asymmetric Traveling Salesman Problem (ATSP), wherein a drone seeks for the time-optimal energy-feasible tour that visits all the target sites and refuels whenever necessary. (3) We devise an efficient approximation algorithm with provable worst-case performance guarantees and implement it in a drone management system, which supports real-time flight path tracking and re-computation in dynamic environments. (4) The effectiveness and practicality of the proposed approach are validated through extensive numerical simulations as well as real-world experiments.

cs.RO↗

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↗