The complexity of scheduling TV commercials

Hägele, K.; Dúnlaing, Colm Ó; Riis, Søren

doi:10.1016/s1571-0661(05)80043-x

Cited by 7 publications

(5 citation statements)

References 4 publications

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“…It is clear that (M2P1N)-SAT belongs to NP. To demonstrate NP-completeness, we show a polynomial-time reduction from the NP-complete problem called BALANCED-3SAT [24]. BALANCED-3SAT is a restriction of the satisfiability problem to boolean expressions in conjunctive normal form where, for each variable x, the positive literal x appears the same number of times as the negative literal x.…”

Section: Lemma 2 (M2p1n)-sat Is Np-completementioning

confidence: 99%

Better Hardness Results for the Minimum Spanning Tree Congestion Problem

Luu

Chrobák

2023

Preprint

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In the spanning tree congestion problem, given a connected graph G, the objective is to compute a spanning tree T in G that minimizes its maximum edge congestion, where the congestion of an edge e of T is the number of edges in G for which the unique path in T between their endpoints traverses e. The problem is known to be NP-hard, but its approximability is still poorly understood, and it is not even known whether the optimum solution can be efficiently approximated with ratio o(n). In the decision version of this problem, denoted K-STC, we need to determine if G has a spanning tree with congestion at most K. It is known that K-STC is NP-complete for K ≥ 8, and this implies a lower bound of 1.125 on the approximation ratio of minimizing congestion. On the other hand, 3-STC can be solved in polynomial time, with the complexity status of this problem for K ∈ 4,5,6,7 remaining an open problem. We substantially improve the earlier hardness results by proving that K-STC is NP-complete for K ≥ 5. This leaves only the case K=4 open, and improves the lower bound on the approximation ratio to 1.2. Motivated by evidence that minimizing congestion is hard even in trees of small constant radius, we also consider K-STC restricted to graphs of radius 2, and we prove that this variant is NP-complete for all K ≥ 6.

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Section: Lemma 2 (M2p1n)-sat Is Np-completementioning

confidence: 99%

Better Hardness Results for the Minimum Spanning Tree Congestion Problem

Luu

Chrobák

2023

Preprint

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“…• It is a rule of TV advertising that competing products or services should not be advertised within the same advertising breaks (Hägele, Dunlaing, and Riis 2001). Therefore, to increase the effectiveness of advertising, competing commercials are not allocated to the same advertising breaks.…”

Section: Ca-based Mechanism For Scheduling Tv Commercialsmentioning

confidence: 99%

“…Brown (1969) described various hardships in scheduling commercials manually, and he developed an algorithm for the exchange of commercials of different lengths between advertising breaks to gain space for other commercials. Hägele, Dunlaing, and Riis (2001) proved that the problem which was defined by Brown is NP-complete. Bollapragada et al (2002), Bollapragada, Bussieck and Mallik (2004a), studied the commercial scheduling problem to generate sales plans to meet the requirements of a single advertiser.…”

Section: Introductionmentioning

confidence: 99%

Scheduling TV commercials using genetic algorithms

Tari

Alaei

2013

International Journal of Production Research

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In this paper, the problem of scheduling commercial messages during the peak of viewing time of a TV channel is formulated as a combinatorial auction-based mathematical programming model. Through this model, a profitable and efficient mechanism for allocating the advertising time to advertisers is developed by which the revenue of TV channels is maximised while the effectiveness of advertising is increased. We developed a steady-state genetic algorithm to find an optimal or a near optimal solution for the proposed problem. A computational experiment was conducted for evaluating the efficiency of the proposed algorithm. A set of test problems with different sizes were generated, using the pseudorandom generation mechanism, and solved by the proposed genetic algorithm. The optimal solutions of the linear programming relaxation of these test problems were also obtained and were used for evaluating the quality of solutions obtained by the developed algorithm. The results of this computational experiment revealed the robustness of the solutions and acceptably low computational time for obtaining these solutions. The computational results also demonstrated that the proposed genetic algorithm had an appropriate ability to preserve population diversity during the search and was capable of obtaining high-quality solutions for the proposed problem. IntroductionTelevision plays an important role in transmitting advertising messages. Although the television industry is mainly an entertainment provider, it takes advantage of the large number of viewers to convey advertising messages. Therefore advertising is the primary source of revenue for TV industries and they are extremely dependent on advertising income. In early days, television programmes were owned by advertisers, today however, it is rare for an entire programme to be sponsored by one advertiser. Rather, TV networks sell the time slots for ads during an entertainment programme.One of the major problems faced by TV channels is how to schedule the commercials in advertising breaks in order to maximise their revenues. The problem is difficult because of limited advertising time and the existence of some constraints that should be considered to maintain the effectiveness of advertising. Hence, we gain the advantages of a profitable and efficient resource allocation mechanism called combinatorial auction (CA) to formulate this problem.Combinatorial auctions involve a single bid taker allocating multiple distinguishable items amongst a set of bidders. Unlike traditional auctions, in CAs bidders can place bids on combinations of items, called packages (bundles), rather than just individual items in order to express more complex preferences. There might be economic relations between items in an auction. Therefore, valuations on packages of items can be super-or sub-additive. We call this, complimentarily and substitutability, respectively. The items may be (1) complements: the value of a bundle is greater than the sum of the values of its parts (e.g. a construction company ...

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“…We also plan to extend the advertisement selection function to enable insertion of multiple advertisements. We will need to investigate ways to schedule multiple advertisements and to avoid advertising competing products in the same timeslot [23].…”

Section: Future Workmentioning

confidence: 99%

Personalized advertisement-duration control for streaming delivery

Oshiba

Koike

Tabuchi

et al. 2002

Proceedings of the Tenth ACM International Conference on Multimedia

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This paper describes the development of a streaming advertisement delivery system that controls the insertion of streaming advertisements into streaming content.Conventional personalization techniques lack a time-control function for advertisement insertion, so the advertisement exposure for each user access can become excessive, much to the annoyance of viewers. This could devalue streaming content by making it less attractive.In our technique, advertisement insertion control is based on the history of each viewer. This personalization method makes it possible to maintain a balanced ratio of the advertisement length to the content length. As a result, our technique should encourage the growth of Internet streaming services and enable more effective and less intrusive advertising.

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The complexity of scheduling TV commercials

Cited by 7 publications

References 4 publications

Better Hardness Results for the Minimum Spanning Tree Congestion Problem

Better Hardness Results for the Minimum Spanning Tree Congestion Problem

Scheduling TV commercials using genetic algorithms

Personalized advertisement-duration control for streaming delivery

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