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Near-Optimal Asymmetric Binary Matrix Partitions

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2016 Algorithmica  
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in takeit-or-leave-it sales. Instances of the problem consist of an n × m binary matrix A and a probability distribution over its columns. A partition scheme B = (B 1 , ..., B n ) consists of a partition B i for each row i of A. The partition B i acts as a smoothing operator on row i that distributes the
more » ... d value of each partition subset proportionally to all its entries. Given a scheme B that induces a smooth matrix A B , the partition value is the expected maximum column entry of A B . The objective is to find a partition scheme such that the resulting partition value is maximized. We present a 9/10approximation algorithm for the case where the probability distribution is uniform and a (1 − 1/e)approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization. The objective of the asymmetric binary matrix partition problem is to find a partition scheme B such that the resulting partition value v B (A, p) is maximized. Alon et al. [2] were the first to consider the asymmetric matrix partition problem. They proved that the problem is APX-hard and provided a 0.563and a 1/13-approximation for uniform and nonuniform probability distributions, respectively. They also considered input matrices with non-negative non-binary entries and presented a 1/2and an Ω(1/ log m)-approximation algorithm for uniform and non-uniform distributions, respectively. This interesting combinatorial optimization problem has apparent relations to revenue maximization in take-it-or-leave-it sales. For example, consider the following setting. There are m items and n potential buyers. Each buyer has a value for each item. Nature selects at random (according to some probability distribution) an item for sale and, then, the seller approaches the highest valuation buyer and offers the item to her at a price equal to her valuation. Can the seller exploit the fact that she has much more accurate information about the items for sale compared to the potential buyers? In particular, information asymmetry arises since the seller knows the realization of the randomly selected item whereas the buyers do not. The approach that is discussed in [2] is to let the seller define a buyer-specific signaling scheme. That is, for each buyer, the seller can partition the set of items into disjoint subsets (bundles) and report this partition to the buyer. After nature's random choice, the seller can reveal to each buyer the bundle that contains the realization, thus enabling her to update her valuation beliefs. The relation of this problem to asymmetric matrix partition should be apparent. Interestingly, the seller can achieve revenue from items for which no buyer has any value. This scenario falls within the line of research that studies the impact of information asymmetry to the quality of markets. Akerlof [1] was the first to introduce a formal analysis of "markets of lemons", where the seller has more information than the buyers regarding the quality of the products. Crawford and Sobel [7] studied how, in such markets, the seller can exploit her advantage in order to maximize revenue. In [17] , Milgrom and Weber provided the "Linkage Principle" which states that the expected revenue is enhanced when bidders are provided with more information. This principle seems to suggest full transparency but, in [15] and [16] the authors suggest that careful bundling of the items is the best way to exploit information asymmetry. Many different frameworks that reveal information to the bidders have been proposed in the literature. More recently, Ghosh et al. [12] considered full information and proposed a clustering scheme according to which, the items are partitioned into bundles and then, for each such bundle, a separate second-price auction is performed. In this way, the potential buyers cannot bid only for the items that they actually want; they also have to compete for items that they do not care. Hence, the demand for each item is increased and the revenue generated is more. Emek et al. [10] present complexity results in similar settings and Miltersen and Sheffet [19] considered fractional bundling schemes for signaling. In this work we focus on the simplest binary case of asymmetric matrix partition which has been proved to be APX-hard. We present a 9/10-approximation algorithm for the uniform case and a (1 − 1/e)-approximation algorithm for non-uniform distributions. Both results significantly improve previous bounds of Alon et al. [2] . The analysis of our first algorithm is quite interesting because, despite its purely combinatorial nature, it exploits linear programming techniques. Similar techniques have been used in a series of papers on variants of set cover (e.g. [3, 4, 5, 6] ) by the second author; however, the application of the technique in the current context requires a quite involved reasoning about the structure of the solutions computed by the algorithm. In our second result, we exploit a nice relation of the problem to submodular welfare maximization and use well-known algorithms from the literature. First, we discuss the application of a simple greedy 1/2-approximation algorithm that has been studied by Lehmann et al. [14] and then apply Vondrák's smooth greedy algorithm [20] to achieve a (1 − 1/e)-approximation. Vondrák's algorithm is optimal in the value query model as Khot et al. [13] have proved. In a more powerful model where it is assumed that demand queries can be answered efficiently, Feige and Vondrák [11] have proved that (1 − 1/e + ǫ)approximation algorithms -where ǫ is a small positive constant -are possible. We briefly discuss the
doi:10.1007/s00453-016-0238-4 fatcat:6axdy5i7vrdzpf6pw45gwoe3vm

Near-Optimal Asymmetric Binary Matrix Partitions [chapter]

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2015 Lecture Notes in Computer Science  
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in takeit-or-leave-it sales. Instances of the problem consist of an n × m binary matrix A and a probability distribution over its columns. A partition scheme B = (B 1 , ..., B n ) consists of a partition B i for each row i of A. The partition B i acts as a smoothing operator on row i that distributes the
more » ... d value of each partition subset proportionally to all its entries. Given a scheme B that induces a smooth matrix A B , the partition value is the expected maximum column entry of A B . The objective is to find a partition scheme such that the resulting partition value is maximized. We present a 9/10approximation algorithm for the case where the probability distribution is uniform and a (1 − 1/e)approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization. The objective of the asymmetric binary matrix partition problem is to find a partition scheme B such that the resulting partition value v B (A, p) is maximized. Alon et al. [2] were the first to consider the asymmetric matrix partition problem. They proved that the problem is APX-hard and provided a 0.563and a 1/13-approximation for uniform and nonuniform probability distributions, respectively. They also considered input matrices with non-negative non-binary entries and presented a 1/2and an Ω(1/ log m)-approximation algorithm for uniform and non-uniform distributions, respectively. This interesting combinatorial optimization problem has apparent relations to revenue maximization in take-it-or-leave-it sales. For example, consider the following setting. There are m items and n potential buyers. Each buyer has a value for each item. Nature selects at random (according to some probability distribution) an item for sale and, then, the seller approaches the highest valuation buyer and offers the item to her at a price equal to her valuation. Can the seller exploit the fact that she has much more accurate information about the items for sale compared to the potential buyers? In particular, information asymmetry arises since the seller knows the realization of the randomly selected item whereas the buyers do not. The approach that is discussed in [2] is to let the seller define a buyer-specific signaling scheme. That is, for each buyer, the seller can partition the set of items into disjoint subsets (bundles) and report this partition to the buyer. After nature's random choice, the seller can reveal to each buyer the bundle that contains the realization, thus enabling her to update her valuation beliefs. The relation of this problem to asymmetric matrix partition should be apparent. Interestingly, the seller can achieve revenue from items for which no buyer has any value. This scenario falls within the line of research that studies the impact of information asymmetry to the quality of markets. Akerlof [1] was the first to introduce a formal analysis of "markets of lemons", where the seller has more information than the buyers regarding the quality of the products. Crawford and Sobel [7] studied how, in such markets, the seller can exploit her advantage in order to maximize revenue. In [17] , Milgrom and Weber provided the "Linkage Principle" which states that the expected revenue is enhanced when bidders are provided with more information. This principle seems to suggest full transparency but, in [15] and [16] the authors suggest that careful bundling of the items is the best way to exploit information asymmetry. Many different frameworks that reveal information to the bidders have been proposed in the literature. More recently, Ghosh et al. [12] considered full information and proposed a clustering scheme according to which, the items are partitioned into bundles and then, for each such bundle, a separate second-price auction is performed. In this way, the potential buyers cannot bid only for the items that they actually want; they also have to compete for items that they do not care. Hence, the demand for each item is increased and the revenue generated is more. Emek et al. [10] present complexity results in similar settings and Miltersen and Sheffet [19] considered fractional bundling schemes for signaling. In this work we focus on the simplest binary case of asymmetric matrix partition which has been proved to be APX-hard. We present a 9/10-approximation algorithm for the uniform case and a (1 − 1/e)-approximation algorithm for non-uniform distributions. Both results significantly improve previous bounds of Alon et al. [2] . The analysis of our first algorithm is quite interesting because, despite its purely combinatorial nature, it exploits linear programming techniques. Similar techniques have been used in a series of papers on variants of set cover (e.g. [3, 4, 5, 6] ) by the second author; however, the application of the technique in the current context requires a quite involved reasoning about the structure of the solutions computed by the algorithm. In our second result, we exploit a nice relation of the problem to submodular welfare maximization and use well-known algorithms from the literature. First, we discuss the application of a simple greedy 1/2-approximation algorithm that has been studied by Lehmann et al. [14] and then apply Vondrák's smooth greedy algorithm [20] to achieve a (1 − 1/e)-approximation. Vondrák's algorithm is optimal in the value query model as Khot et al. [13] have proved. In a more powerful model where it is assumed that demand queries can be answered efficiently, Feige and Vondrák [11] have proved that (1 − 1/e + ǫ)approximation algorithms -where ǫ is a small positive constant -are possible. We briefly discuss the
doi:10.1007/978-3-662-48054-0_1 fatcat:pwrjxinozffvjf7sjsrbf7hdj4

Preemptive Coordination Mechanisms for Unrelated Machines [chapter]

Fidaa Abed, Chien-Chung Huang
2012 Lecture Notes in Computer Science  
We investigate coordination mechanisms that schedule n jobs on m unrelated machines. The objective is to minimize the latest completion of all jobs, i.e., the makespan. It is known that if the mechanism is non-preemptive, the price of anarchy is Ω(log m). Both Azar, Jain, and Mirrokni (SODA 2008) and Caragiannis (SODA 2009) raised the question whether it is possible to design a coordination mechanism that has constant price of anarchy using preemption. We give a negative answer. All
more » ... c coordination mechanisms, if they are symmetric and satisfy the property of independence of irrelevant alternatives, even with preemption, have the price of anarchy Ω( log m log log m ). Moreover, all randomized coordination mechanisms, if they are symmetric and unbiased, even with preemption, have similarly the price of anarchy Ω( log m log log m ). Our lower bound complements the result of Caragiannis, whose bcoord mechanism guarantees O( log m log log m ) price of anarchy. Our lower bound construction is surprisingly simple. En route we prove a Ramsey-type graph theorem, which can be of independent interest. On the positive side, we observe that our lower bound construction critically uses the fact that the inefficiency of a job on a machine can be unbounded. If, on the other hand, the inefficiency is not unbounded, we demonstrate that it is possible to break the Ω( log m log log m ) barrier on the price of anarchy by using known coordination mechanisms.
doi:10.1007/978-3-642-33090-2_3 fatcat:h3aj4ft2efa53d6rhnir5hzypy

Optimal Coordination Mechanisms for Multi-job Scheduling Games [chapter]

Fidaa Abed, José R. Correa, Chien-Chung Huang
2014 Lecture Notes in Computer Science  
Abed, J.R. Correa, and C.-C. Huang  ...  The result was finally established by Abed and Huang [1] , who proved that no symmetric coordination mechanism satisfying the so-called "independence of irrelevant alternatives" property, even if preemption  ... 
doi:10.1007/978-3-662-44777-2_2 fatcat:er4cerba5jalvjxcszhrz55pay

Near-optimal asymmetric binary matrix partitions [article]

Fidaa Abed, Ioannis Caragiannis, Alexandros A. Voudouris
2015 arXiv   pre-print
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an n × m binary matrix A and a probability distribution over its columns. A partition scheme B=(B_1,...,B_n) consists of a partition B_i for each row i of A. The partition B_i acts as a smoothing operator on row i that distributes the expected
more » ... ue of each partition subset proportionally to all its entries. Given a scheme B that induces a smooth matrix A^B, the partition value is the expected maximum column entry of A^B. The objective is to find a partition scheme such that the resulting partition value is maximized. We present a 9/10-approximation algorithm for the case where the probability distribution is uniform and a (1-1/e)-approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization.
arXiv:1407.8170v3 fatcat:tr5jcdbmwvdcvhn7wyvxgxn7ri

A linear delay algorithm for enumerating all connected induced subgraphs

Mohammed Alokshiya, Saeed Salem, Fidaa Abed
2019 BMC Bioinformatics  
Real biological and social data is increasingly being represented as graphs. Pattern-mining-based graph learning and analysis techniques report meaningful biological subnetworks that elucidate important interactions among entities. At the backbone of these algorithms is the enumeration of pattern space. Results: We propose an efficient algorithm for enumerating all connected induced subgraphs of an undirected graph. Building on this enumeration approach, we propose an algorithm for mining all
more » ... ximal cohesive subgraphs that integrates vertices' attributes with subgraph enumeration. To efficiently mine all maximal cohesive subgraphs, we propose two pruning techniques that remove futile search nodes in the enumeration tree. Conclusions: Experiments on synthetic and real graphs show the effectiveness of the proposed algorithm and the pruning techniques. On enumerating all connected induced subgraphs, our algorithm is several times faster than existing approaches. On dense graphs, the proposed approach is at least an order of magnitude faster than the best existing algorithm. Experiments on protein-protein interaction network with cancer gene dysregulation profile show that the reported cohesive subnetworks are biologically interesting.
doi:10.1186/s12859-019-2837-y fatcat:wvfiqia3ijfxtcgt2om56dniia

Scheduling Maintenance Jobs in Networks [article]

Fidaa Abed and Lin Chen and Yann Disser and Martin Groß and Nicole Megow and Julie Meißner and Alexander T. Richter and Roman Rischke
2017 arXiv   pre-print
We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines. We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral
more » ... points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions. Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.
arXiv:1701.08809v1 fatcat:lzelw76snnal7ldiryawcalkjy

On Guillotine Cutting Sequences

Fidaa Abed, Parinya Chalermsook, José Correa, Andreas Karrenbauer, Pablo Pérez-Lantero, José A. Soto, Andreas Wiese, Marc Herbstritt
2015 International Workshop on Approximation Algorithms for Combinatorial Optimization  
the set of unit squares such that the lower left corner of S(i, j) is at coordinates i · (1, δ) + j · (−δ, 1) = (i − jδ, j + iδ), where δ is an arbitrarily small positive constant (say, smaller than 1/(ab  ... 
doi:10.4230/lipics.approx-random.2015.1 dblp:conf/approx/AbedCCKPSW15 fatcat:ynl7thv55natvptlcx6duuyip4

Diagnosis of Adrenal Insufficiency in Severe Sepsis and Septic Shock

Djillali Annane, Virginie Maxime, Fidaa Ibrahim, Jean Claude Alvarez, Emuri Abe, Philippe Boudou
2006 American Journal of Respiratory and Critical Care Medicine  
Rationale: Diagnosis of adrenal insufficiency in critically ill patients has relied on random or cosyntropin-stimulated cortisol levels, and has not been corroborated by a more accurate diagnostic standard. Objective: We used the overnight metyrapone stimulation test to investigate the diagnostic value of the standard cosyntropin stimulation test, and the prevalence of sepsis-associated adrenal insufficiency. Methods: This was an inception cohort study. Measurements and Results: In two
more » ... ve septic cohorts (n ϭ 61 and n ϭ 40), in 44 patients without sepsis and in 32 healthy volunteers, we measured (1 ) serum cortisol before and after cosyntropin stimulation, albumin, and corticosteroid-binding globulin levels, and (2) serum corticotropin, cortisol, and 11␤-deoxycortisol levels before and after an overnight metyrapone stimulation. Adrenal insufficiency was defined by postmetyrapone serum 11␤-deoxycortisol levels below 7 g/dl. More patients with sepsis (31/61 [59% of original cohort with sepsis] and 24/40 [60% of validation cohort with sepsis]) met criteria for adrenal insufficiency than patients without sepsis (3/44; 7%) (p Ͻ 0.001 for both comparisons). Baseline cortisol (Ͻ 10 g/dl), ⌬ cortisol (Ͻ 9 g/dl), and free cortisol (Ͻ 2 g/dl) had a positive likelihood ratio equal to infinity, 8.46 (95% confidence interval, 1.19-60.25), and 9.50 (95% confidence interval, 1.05-9.54), respectively. The best predictor of adrenal insufficiency (as defined by metyrapone testing) was baseline cortisol of 10 g/dl or less or ⌬ cortisol of less than 9 g/dl. The best predictors of normal adrenal response were cosyntropin-stimulated cortisol of 44 g/dl or greater and ⌬ cortisol of 16.8 g/dl or greater. Conclusions: In sepsis, adrenal insufficiency is likely when baseline cortisol levels are less than 10 g/dl or delta cortisol is less than 9 g/dl, and unlikely when cosyntropin-stimulated cortisol level is 44 g/dl or greater or ⌬ cortisol is 16.8 g/dl or greater.
doi:10.1164/rccm.200509-1369oc pmid:16973979 fatcat:r3zn6ykbd5etxhyjxxzkjgvycy

Coordinating selfish players in scheduling games [article]

Fidaa Abed, Universität Des Saarlandes, Universität Des Saarlandes
2015
We investigate coordination mechanisms that schedule n jobs on m unrelated machines. The objective is to minimize the makespan. It was raised as an open question whether it is possible to design a coordination mechanism that has constant price of anarchy using preemption. We give a negative answer. Next we introduce multi-job players that control a set of jobs, with the aim of minimizing the sum of the completion times of theirs jobs. In this setting, previous mechanisms designed for players
more » ... h single jobs are inadequate, e.g., having large price of anarchy, or not guaranteeing pure Nash equilibria. To meet this challenge, we design three mechanisms that induce pure Nash equilibria while guaranteeing relatively small price of anarchy.
doi:10.22028/d291-26614 fatcat:hrgddyrrvbgrrbizgclhhz5hjq

Page 106 of Annals of Mathematics Vol. 12, Issue 4 [page]

1898 Annals of Mathematics  
DG)(9D) (GD) 8 L < | “mn /fiDaA? ! —_ ” | ¢ Z| si | DAL Lg!)  ...  .(¢'0) = 92h, P7)( 9D) 2,9,V (9D) GV) D 9I z iP f@r7} bled Abe gla) (40) ( glo) > 2.992 ,P9)2(,.9,0)(90).(9D) "9 CT ) 2 gi L § ed | Po M Ae!  ... 

Page 39 of Newsletter on Intellectual Freedom Vol. 57, Issue 6 [page]

2008 Newsletter on Intellectual Freedom  
The first of the students—Fidaa Abed, a 23-year-old computer-science master’s student who plans to enroll at the University of California at San Diego—was granted a U.S. visa on July 28.  ...  Abed said. adding that the official had told him that he had never heard of such a thing happening.  ... 

Page 189 of Edinburgh Magazine Vol. 3, Issue [page]

1759 Edinburgh Magazine  
|aughmg Ipring; Eden’s delights 1 wHii'ch be ab>ne cooM mg. Yet not thele fcencs could bound hit daring flighf, >’■ Born to the tafli he role a nobler height.  ...  TheoAer ccalii; tw tremble on thy fidaa \ Let thy calm, waters gouUy Heal alooig, • Pen ham ihhhomagecLims while ha ii>4>ir<s my Caig, . \ Far as thy billows roll. diipersM away T'o dillanc climes, the  ... 

Page 3473 of Psychological Abstracts Vol. 93, Issue 9 [page]

2006 Psychological Abstracts  
., 24981 Almomani, Fidaa, 26804 Aloisi, Anna Maria, 25067 Alonso, Pino, 26680 Alonso-Navarro, Hortensia, 26264, 26652 Alper, Kenneth, 27028 Alper, S.  ...  Yasantha, 26090 Arkin, Robert M., 25697 Arkoff, Abe, 27234 Arlinger, Stig, 24570 Arman, Fehim, 26444, 26456 Armitage, Christopher J., 27490 Armstrong, Vickie L Arndt, Jason, 24848 Armett, Dennis B., 26349  ... 

FAKTOR-FAKTOR KEPUASAN PELANGGAN DAN LOYALITAS PELANGGAN (LITERATURE REVIEW MANAJEMEN PEMASARAN)

Sambodo Rio Sasongko
2021 Jurnal Ilmu Manajemen Terapan  
Alnaser, Feras & Ghani, Mazuri & Rahi, Samar & Mansour, Majeed & Abed, Hussein. (2017).  ...  Kualitas pelayanan ini sudah banyak di teliti oleh peneliti sebelumnya di antaranya adalah Adriany, Vita. (2018), Al Rasyid, Harun dan Erica, Denny (2018), Safi, Fidaa O.D dan Alagha, Marwan S (2020),  ... 
doi:10.31933/jimt.v3i1.707 fatcat:vvvvikazxbfrreoponomfohmni
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