The Sum Of Absolute Differences On A Network: Algorithm And Comparison With Other Equality Measures
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
AbstractIn this work, we address a double objective. In the first place, we study the problem of locating a single facility on a network N(V,E) which minimizes the sum of absolute differences between all pairs of weighted travel distances from the users to the facility, and we propose an O (|E|V|2log |V|)) algorithm for solving it. Likewise, we present a computational experience in which we compare the behavior of several equality measures by means of the placement of their respective optimal locations. To this end we define a measure of relative proximity between two optima, and we analyze the results obtained by considering several setting models of the network.RésuméCe travail poursuit un double objectif: nous étudions d’abord le problème concernant la localisation d’une facilité sur un réseau qui minimise l’addition des différences absolues entre toutes les paires de distances pondérées des usagers au facilité, et nous proposons une algorithme de temps O(|E||V|2log |V|) pour le résoudre. Nous présentons également une expérience computationnelle où nous comparons le comportement de plusieurs mesures d’égalité, au moyen de l’emplacement des respectives localisations optimales. Pour ce faire, nous définissons une mesure de proximité relative entre deux optima et nous analysons les résultats obtenus pour plusieurs modèles de réseaux.Key words:: FacilityLocationNetworksEquality criterionMots-clés:: FacilitéLocalisationRéseauCritère d’égalité Additional informationNotes on contributorsMa Cruz López-De-Los-MozosMa Cruz López-de-los-Mozos is a Lecturer of the University School in the Applied Mathematics I Department at the University of Sevilla, Spain. She received a Master of Science at the Complutense University of Madrid and a PhD in Mathematics at the University of Sevilla. Her main research interest is location analysis with equality measures. She has published in the European Journal of Operational Research, the Journal of the Operational Research Society, RAIRO Operations Research and Studies in Locational Analysis.Juan A. MesaJuan A. Mesa is a Professor in the Applied Mathematics Department II at the University of Sevilla. He holds a Master of Science and a PhD in Mathematics from the University of Sevilla. He has published in Computers & Operations Research, Discrete Applied Mathematics, European Journal of Operational Research, International Journal of Industrial Engineering, the Journal of Advanced Transportation, the Journal of the Operational Research Society and Studies in Locational Analysis, among others. His research interests include location of extensive facilities both in networks and continuous spaces, location of facilities with undesirable effects and metro network design. He has been the main researcher of several projects and, in particular, he is the coordinator of the Spanish Thematic Network on Locational Analysis and its Applications.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it