On the black-box complexity of Sperner's Lemma

We present several results on the complexity of various forms of Sperner's Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an $O(\sqrt{n})$ deterministic query algorithm for the black-box version of the problem {\bf 2D-SPERNER}, a well studied member of Papadimitriou's complexity class PPAD. This upper bound matches the $\Omega(\sqrt{n})$ deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an $\Omega(\sqrt[4]{n})$ lower bound for its probabilistic, and an $\Omega(\sqrt[8]{n})$ lower bound for its quantum query complexity, showing that all these measures are polynomially related.Comment: 16 pages with 1 figur

Finding Nash equilibria of bimatrix games

This thesis concerns the computational problem of finding one Nash equilibrium of a bimatrix game, a two-player game in strategic form. Bimatrix games are among the most basic models in non-cooperative game theory, and finding a Nash equilibrium is important for their analysis. The Lemke—Howson algorithm is the classical method for finding one Nash equilib-rium of a bimatrix game. In this thesis, we present a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labelled facets in d-space. The construc-tion is extended to two classes of non-square games where, in addition to exponentially long Lemke—Howson computations, finding an equilibrium by support enumeration takes exponential time on average. The Lemke—Howson algorithm, which is a complementary pivoting algorithm, finds at least one solution to the linear complementarity problem (LCP) derived from a bimatrix game. A closely related complementary pivoting algorithm by Lemke solves more general LCPs. A unified view of these two algorithms is presented, for the first time, as far as we know. Furthermore, we present an extension of the standard version of Lemke's algorithm that allows one more freedom than before when starting the algorithm

Design of efficient constant weight codes

In a constant weight code, each code word contains a constant number of 1's. If this number is equal to half the length of the code word then the code is called balanced. These codes find many applications in computer and communication systems noise reduction in VLSI systems, fault masking in bus lines of VLSI systems, rejection of the low frequency components in digital communication systems, delay insensitive communications in asynchronous systems, data transmission in fiber optics, data storage in optical discs and magnetic tapes, fault tolerant synchronous circuits, etc. This thesis presents new efficient design methods for constant weight codes suitable to these applications. The proposed codes require low redundancy but at the same time have fast and simple encoding/decoding algorithms

On location, domination and information retrieval

The thesis is divided into two main branches: identifying and locatingdominating codes, and information retrieval. The former topics are motivated by the aim to locate objects in sensor networks (or other similar applications) and the latter one by the need to retrieve information in memories such as DNA data storage systems. Albeit the underlying applications, the study on these topics mainly belongs to discrete mathematics; more specically, to the elds of coding and graph theory. The sensor networks are usually represented by graphs where vertices represent the monitored locations and edges the connections between the locations. Moreover, the locations of the sensors are determined by a code. Furthermore, the desired properties of the sensor network are deeply linked with the properties of the underlying code. The number of errors in reading the data is abundant in the DNA data storage systems. In particular, there can occur more errors than a reasonable error-correcting code can handle. However, this problem is somewhat oset by the possibility to obtain multiple approximations of the same information from the data storage. Hence, the information retrieval process can be modelled by the Levenshtein's channel model, where a message is sent through multiple noisy channels and multiple outputs are received. In the rst two papers of the thesis, we introduce and study the new concepts of self- and solid-locating-dominating codes as a natural analogy to self-identifying codes with respect to locating-dominating codes. The rst paper introduces these new codes and considers them in some graphs such as the Hamming graphs. Then, in the second paper, we broaden our view on the topic by considering graph theoretical questions. We give optimal codes in multiple dierent graph classes and some more general results using concepts such as the Dilworth number and graph complements. The third paper focuses on the q-ary Hamming spaces. In particular, we disprove a conjecture proposed by Goddard and Wash related to identifying codes. In the fourth paper, we return to self- and solid-locating-dominating codes and give optimal codes in some graph classes and consider their densities in innite graphs. In the fth paper, we consider information retrieval in memories; in particular, the Levenshtein's channel model. In the channel model, we transmit some codeword belonging to the binary Hamming space through multiple identical channels. With the help of multiple dierent outputs, we give a list of codewords which may have been sent. In the paper, we study the number of channels required to have a rather small (constant) list size when the properties of the channels, the code and the dimension of the Hamming space are xed. In particular, we give an exact relation between the number of channels and the asymptotic value of the maximum list size.Väitöskirja käsittelee kahta aihetta: identioivia ja paikantavia peittokoodeja sekä tiedon noutamista muistista. Ensimmäisen aiheen motivaationa on objektien paikantaminen sensoriverkoista (sekä muut samankaltaiset sovellukset) ja jälkimmäisen tiedonnouto DNA-muisteista. Näiden aiheiden tutkimus kuuluu diskreettiin matematiikkaan, täsmällisemmin koodaus- ja graa-teoriaan. Sensoriverkkoja kuvataan yleensä graafeilla, joissa solmut esittävät tarkkailtuja kohteita ja viivat yhteyksiä näiden kohteiden välillä. Edelleen sensorien paikat määräytyvät annetun koodin perusteella. Tästä johtuen sensoriverkon halutut ominaisuudet pohjautuvat vahvasti alla olevaan koodiin. Luettaessa tietoa DNA-muisteista tapahtuvien virheiden määrä saattaa olla erittäin suuri; erityisesti suurempi kuin kiinnitetyn virheitä korjaavan koodin korjauskyky. Toisaalta tilanne ei ole aivan näin ongelmallinen, sillä DNA-muisteista voidaan saada useita eri arvioita muistiin tallennetusta tiedosta. Näistä syistä johtuen tietojen noutamista DNA-muisteista voidaan mallintaa käyttäen Levenshteinin kanavamallia. Kanavamallissa yksi viesti lähetetään useiden häiriöisten kanavien kautta ja näin vastaanotetaan useita viestejä (yksi jokaisesta kanavasta). Väitöskirjan kahdessa ensimmäisessä julkaisussa esitellään ja tutkitaan uusia paikantavien peittokoodien luokkia, jotka pohjautuvat aiemmin tutkittuihin itse-identioiviin koodeihin. Ensimmäisessä julkaisussa on esitelty nämä koodiluokat sekä tutkittu niitä joissain graafeissa kuten Hammingin graafeissa. Tämän jälkeen toisessa julkaisussa käsitellään yleisiä graa-teoreettisia kysymyksiä. Julkaisussa esitetään optimaaliset koodit useille graaperheille sekä joitain yleisempiä tuloksia käyttäen mm. Dilworthin lukua sekä graakomplementteja. Kolmas julkaisu keskittyy q-arisiin Hammingin avaruuksiin. Erityisesti julkaisussa todistetaan vääräksi Goddardin ja Washin aiemmin esittämä identioivia koodeja koskeva otaksuma. Neljäs artikkeli käsittelee jo kahdessa ensimmäisessä artikkelissa esiteltyjä paikantavien peittokoodien luokkia. Artikkeli esittää optimaalisia koodeja useille graaperheille sekä käsittelee äärettömiä graafeja. Viides artikkeli käsittelee tiedonnoutoa ja erityisesti Levenshteinin kanavamallia. Kanavamallissa binääriseen Hammingin avaruuteen kuuluva koodisana lähetetään useiden identtisten kanavien läpi. Näistä kanavista vastaanotetaan useita eri arvioita lähetetystä koodisanasta ja rakennetaan lista mahdollisesti lähetetyistä sanoista. Artikkelissa tutkitaan kuinka monta kanavaa tarvitaan, jotta tämän listan koko on pieni (vakio), kun kanavien ominaisuudet, koodi ja Hammingin avaruuden dimensio on kiinnitetty. Erityisesti löydetään täsmällinen suhde kanavien lukumäärän ja asymptoottisesti maksimaalisen listan koon välille

Publications of the Jet Propulsion Laboratory, 1978

This bibliography cites 958 externally distributed technical papers released during calendar year 1978, that resulted from scientific and engineering work performed, or managed, by the Jet Propulsion Laboratory. The publications are indexed by author, subject, publication type and number. A descriptive entry appears under the name of each author of each publication; an abstract is included with the entry for the primary (first-listed) author

Truthful and Fair Resource Allocation

How should we divide a good or set of goods among a set of agents? There are various constraints that we can consider. We consider two particular constraints. The first is fairness - how can we find fair allocations? The second is truthfulness - what if we do not know agents valuations for the goods being allocated? What if these valuations need to be elicited, and agents will misreport their valuations if it is beneficial? Can we design procedures that elicit agents' true valuations while preserving the quality of the allocation? We consider truthful and fair resource allocation procedures through a computational lens. We first study fair division of a heterogeneous, divisible good, colloquially known as the cake cutting problem. We depart from the existing literature and assume that agents have restricted valuations that can be succinctly communicated. We consider the problems of welfare-maximization, expressiveness, and truthfulness in cake cutting under this model. In the second part of this dissertation we consider truthfulness in settings where payments can be used to incentivize agents to truthfully reveal their private information. A mechanism asks agents to report their private preference information and computes an allocation and payments based on these reports. The mechanism design problem is to find incentive compatible mechanisms which incentivize agents to truthfully reveal their private information and simultaneously compute allocations with desirable properties. The traditional approach to mechanism design specifies mechanisms by hand and proves that certain desirable properties are satisfied. This limits the design space to mechanisms that can be written down and analyzed. We take a computational approach, giving computational procedures that produce mechanisms with desirable properties. Our first contribution designs a procedure that modifies heuristic branch and bound search and makes it usable as the allocation algorithm in an incentive compatible mechanism. Our second contribution draws a novel connection between incentive compatible mechanisms and machine learning. We use this connection to learn payment rules to pair with provided allocation rules. Our payment rules are not exactly incentive compatibility, but they minimize a measure of how much agents can gain by misreporting.Engineering and Applied Science

End-userApplication for Early Forest Fire Detection and Prevention

n this paper, we describe a Web application that has been designed and implemented by Fulda University of Applied Sciences in the context of the ASPires project. The application extends the functionality available to Crisis Management Centers (CMC). Actual readings from sensors installed in the test areas, for example national parks, are made available to CMC personnel, as well as pictures from cameras that are either mounted on stationary observation towers or taken by Unmanned Aerial Vehicles (UAVs) in the area of an actual of supposed forest fire. Data are transmitted to the Aspires cloud and delivered swiftly to the Web application via an open interface. Furthermore, fire alarms raised by novel detection algorithms are forwarded automatically to the application. This clearly improves the potential for the early detection of forest fires in rural areas